text
stringlengths
2
1.42k
label
int64
0
1
zero cycles; Chow group of algebraic cycles; Hodge structure Hodge conjecture; Tate conjecture on algebraic cycles; absolutely; simple abelian variety; Mumford-Tate group; Mumford-Tate; conjectures Tankeev, SG, Cycles on simple abelian varieties of prime dimension over number fields, Math. USSR Izv., 31, 527, (1988)
0
zero cycles; Chow group of algebraic cycles; Hodge structure torsion subgroup of second Chow group; \(K_2\)-cohomology; Galois module structure; Bloch-Quillen-formula; Neron-Severi group; Picard variety Colliot-Thélène, J. -L.; Raskind, W., \(\mathcal{K}_2\)-cohomology and the second Chow group, Math. Ann., 270, 165-199, (1985)
0
zero cycles; Chow group of algebraic cycles; Hodge structure algebraic cycles; Chow groups; intermediate Jacobians; Abel-Jacobi map; Hodge structures; Bloch-Beilinson conjecture M. Green, P. A. Griffiths, and K. H. Paranjape, Cycles over fields of transcendence degree \(1\) , Michigan Math. J. 52 (2004), 181--187.
0
zero cycles; Chow group of algebraic cycles; Hodge structure zero cycles; Chow group; Grothendieck group Srinivas, V., Torsion 0-cycles on affine varieties in characteristic \textit{p}, J. algebra, 120, 428-432, (1989)
0
zero cycles; Chow group of algebraic cycles; Hodge structure De Rham cohomology; crystalline action of Weil group; Morita's \(p\)-adic gamma function; absolute Hodge cycles; Frobenius matrix of Fermat curves Ogus, A, A \(p\)-adic analogue of the chowla-Selberg formula, \(p\)-adic analysis (Trento, 1989), Lect. Notes Math., 1454, 319-341, (1990)
0
zero cycles; Chow group of algebraic cycles; Hodge structure symposium; proceedings; Kyoto (Japan); deformation of group schemes; Number theory; finite group schemes; Kummer-Artin-Schreier-Witt theory; Galois module structure; algebraic curves; Hopf algebra
0
zero cycles; Chow group of algebraic cycles; Hodge structure filtration on the Chow group; Abel-Jacobi map; regulator; Deligne cohomology; Hodge structure; Jannsen conjecture; Bloch-Beilinson conjecture Lewis, J.: A filtration on the Chow groups of a complex projective variety. Compos. Math. 128(3), 299--322 (2001)
0
zero cycles; Chow group of algebraic cycles; Hodge structure algebraic cycles; etale topology; Homotopy; homology; Chow groups; Bejlinson's conjectures; regulator map; Lichtenbaum's conjectures; Milnor K-groups; Soulé's conjecture; poles of the zeta function Bloch, Spencer, Algebraic cycles and the {B}eĭlinson conjectures, The {L}efschetz Centennial Conference, {P}art {I} ({M}exico {C}ity, 1984), Contemp. Math., 58, 65-79, (1986), Amer. Math. Soc., Providence, RI
0
zero cycles; Chow group of algebraic cycles; Hodge structure Picard number; Lefschetz number; Fermat hypersurface; Delsarte surface; variation of Hodge structure; families of algebraic surfaces
0
zero cycles; Chow group of algebraic cycles; Hodge structure Hodge conjecture; algebraic cycles of codimension 2 Saito, M.: Some remarks on the Hodge type conjecture. In: Motives, Seattle, WA, 1991. Proc. Sympos. Pure Math., vol. 55, pp. 85--100. Am. Math. Soc., Providence (1994)
0
zero cycles; Chow group of algebraic cycles; Hodge structure totally geodesic submanifold; variation of Hodge structure; left quasi-group; Loos-symmetric space; Loos-Hermitian symmetric space
0
zero cycles; Chow group of algebraic cycles; Hodge structure quasi-split unitary group \(U(3)\); cuspidal representation; periods; theta-lift; existence of algebraic cycles; Shimura variety S. Gelbart, J. Rogawski, and D. Soudry, On periods of cusp forms and algebraic cycles for \?(3), Israel J. Math. 83 (1993), no. 1-2, 213 -- 252.
0
zero cycles; Chow group of algebraic cycles; Hodge structure fields of large transcendence degree; algebraic independence; zero lemmas; zero estimate for group varieties; primary ideal; polynomial rings; algebraic subgroups of products of elliptic curves; effective version of Hilbert's Nullstellensatz; Kolchin theorem; Weierstrass elliptic function Masser, D. W.; Wüstholz, G., Fields of large transcendence degree generated by values of elliptic functions, Invent. Math., 72, 3, 407-464, (1983)
0
zero cycles; Chow group of algebraic cycles; Hodge structure algebraic cycles; Chow ring; motives; Bloch-Beilinson filtration; hyperkähler variety; Lagrangian subvariety; constant cycle subvariety; (Hilbert scheme of) \(K3\) surface; Beauville's splitting property; multiplicative Chow-Künneth decomposition; spread of algebraic cycles
0
zero cycles; Chow group of algebraic cycles; Hodge structure variation of polarized Hodge structure; intersection cohomology group; \(L^ 2\)-cohomology group Kashiwara, M.; Kawai, T., \textit{the Poincaré lemma for a variation of polarized Hodge structure}, Proc. Japan Acad. Ser. A Math. Sci., 61, 164-167, (1985)
0
zero cycles; Chow group of algebraic cycles; Hodge structure Chow group; codimension-two cycles of the moduli space C. F. Faber, Some results on the codimension-two Chow group of the moduli space of stable curves , Algebraic curves and projective geometry (Trento, 1988), Lecture Notes in Math., vol. 1389, Springer, Berlin, 1989, pp. 66-75.
0
zero cycles; Chow group of algebraic cycles; Hodge structure Tannakian categories; Hodge cycles; motives; Taniyama group; canonical models; automorphic vector bundles; canonical models of Shimura- varieties; model over a number-field Milne, J. S., Canonical models of (mixed) Shimura varieties and automorphic vector bundles, Automorphic Forms, Shimura Varieties, and \textit{L}-Functions, Vol. I (Ann Arbor, MI, 1988), 283-414, (1990), Academic Press: Academic Press, Boston, MA
0
zero cycles; Chow group of algebraic cycles; Hodge structure intersection number of two divisors; normal surface; bivariant intersection theory; Chow group; rational equivalence; algebraic equivalence S. Kimura, Fractional intersection and bivariant theory, Comm. Algebra 20 (1992), no. 1, 285-302.
0
zero cycles; Chow group of algebraic cycles; Hodge structure abelian variety; Mumford-Tate group; ring of Hodge cycles [9] S. P. White, `` Sporadic cycles on CM abelian varieties {'', \(Compositio Math.\)88 (1993), no. 2, p. 123-142. Numdam | &MR 12 | &Zbl 0798.}
0
zero cycles; Chow group of algebraic cycles; Hodge structure Ritt formal group; Hopf algebra; formalization of algebraic structure; algebra of differential operators; Lie algebras of formal groups W. Nichols and B. Weisfeiler, ''Differential formal groups of J. F. Ritt,''Am. J. Math.,104, 943--1005 (1982).
0
zero cycles; Chow group of algebraic cycles; Hodge structure algebraic cycles; rational equivalence; Chow group; Lieberman Jacobian Lewis J.D. (1993). Cylinder homomorphism and Chow groups. Math. Nachr. 160: 205--221
0
zero cycles; Chow group of algebraic cycles; Hodge structure zero cycles; Bloch conjecture; Albanese variety; Chow group; pushout diagram; 1-motive; Chern classes in Deligne cohomology H. Gillet, On the \(K\)-theory of surfaces with multiple curves and a conjecture of Bloch , Duke Math. J. 51 (1984), no. 1, 195-233.
0
zero cycles; Chow group of algebraic cycles; Hodge structure Hilbert modular surface; Shimura datum; generic Mumford-Tate group; variation of Hodge structure; Hecke correspondence B. Edixhoven, On the André-Oort conjecture for Hilbert modular surfaces, Moduli of abelian varieties (Texel Island 1999), Birkhäuser, Basel (2001), 133-155.
0
zero cycles; Chow group of algebraic cycles; Hodge structure algebraic cycles; Chow group; algebraic surfaces; higher Chow group; indecomposable elements
0
zero cycles; Chow group of algebraic cycles; Hodge structure algebraic cycles; Chow groups; motives; hyperkähler varieties; anti-symplectic involution; \(K3\) surfaces; (double) EPW sextics; Beauville's splitting principle; multiplicative Chow-Kenneth decomposition; spread of algebraic cycles
0
zero cycles; Chow group of algebraic cycles; Hodge structure torsion subgroup in the Chow group; zero cycles; elliptic modular surface; Kummer surface; modular elliptic curve Andreas Langer, 0-cycles on the elliptic modular surface of level 4, Tohoku Math. J. (2) 50 (1998), no. 2, 291 -- 302.
0
zero cycles; Chow group of algebraic cycles; Hodge structure zero cycles of degree zero; rational equivalence; Brauer group Colliot-Thélène, J.-L., L'arithmétique du groupe de Chow des zéro-cycles, J. Théorie de nombres de Bordeaux, 7, 51-73, (1995)
0
zero cycles; Chow group of algebraic cycles; Hodge structure Chow rings; algebraic cycles; motives of abelian type
0
zero cycles; Chow group of algebraic cycles; Hodge structure \(K_1\)-groups of algebraic curves; arithmetic Hodge structure; generalized Jacobian rings
0
zero cycles; Chow group of algebraic cycles; Hodge structure Chow group; Bloch's conjecture; Godeaux surface; algebraic cycles Voisin, Claire, Sur les zéro-cycles de certaines hypersurfaces munies d'un automorphisme, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 19, 4, 473-492, (1992)
0
zero cycles; Chow group of algebraic cycles; Hodge structure intersection ring; Grothendieck group; \(\gamma\)-filtration; rational equivalence; Chow's moving lemma; algebraic cycles; relative Chow group Consani, C., A moving-lemma for a singular variety and applications to the Grothendieck group \(K\)\_{}\{0\}(\(X\)), Santa Margherita Ligure, 1989, Providence
0
zero cycles; Chow group of algebraic cycles; Hodge structure arithmetic structure of Tate-Shafarevich group; algebraic tori; Hasse principle; norm form equations Hürlimann, W., On algebraic tori of norm type, Comment. Math. Helv., 0010-2571, 59, 4, 539-549, (1984)
0
zero cycles; Chow group of algebraic cycles; Hodge structure group of cycles; Chow group; Hilbert-Samuel polynomial; Euler characteristic; multiplicity; intersection multiplicity; homological conjectures; new intersection theorem; Frobenius map; projective scheme of a multigraded ging; Chern class P. ROBERTS. Multiplicities and Chern classes in local algebra, Cambridge University Press (1998). CMP 99:13
0
zero cycles; Chow group of algebraic cycles; Hodge structure quadratic forms; Pfister neighbors; projective quadrics; Chow groups; algebraic cycles; motives of quadrics N.\ A. Karpenko, Characterization of minimal Pfister neighbors via Rost projectors, J. Pure Appl. Algebra 160 (2001), no. 2-3, 195-227.
0
zero cycles; Chow group of algebraic cycles; Hodge structure Hilbert scheme; action of linear solvable group; Chow group; equivariant cycles; rational equivalences Hirschowitz, A.: Le groupe de Chow équivariant. CR acad. Sci. Paris sér. I math. 298, 87-89 (1984)
0
zero cycles; Chow group of algebraic cycles; Hodge structure mixed motives; Hodge conjecture; Hodge structure of geometric origin; Chow groups; cycle class map; correspondence
0
zero cycles; Chow group of algebraic cycles; Hodge structure algebraic cycles; Chow group; Jacobian doi:10.1007/BF03191366
0
zero cycles; Chow group of algebraic cycles; Hodge structure algebraic cycles; correspondence; Chow group; push forward; pull back; abelian variety
0
zero cycles; Chow group of algebraic cycles; Hodge structure theorem of the fixed part; variation of mixed Hodge structure; Mumford- Tate group; abelian integrals André, Y, Mumford-Tate groups of mixed Hodge structures and the theorem of the fixed part, Compos. Math., 82, 1-24, (1992)
0
zero cycles; Chow group of algebraic cycles; Hodge structure Chow group; zero cycles; abelian varieties; Somekawa \(K\)-group; Brauer group Gazaki, Evangelia, On a filtration of \(C H_0\) for an abelian variety, Compos. Math., 151, 3, 435-460, (2015), MR 3320568
0
zero cycles; Chow group of algebraic cycles; Hodge structure categoricity; fundamental group; analytic spaces; complex algebraic variety; bona fide topology; stability; homotopy classes of paths; universal covering space; analytic Zariski structure M. Gavrilovich, Covers of algebraic varieties, preprint
0
zero cycles; Chow group of algebraic cycles; Hodge structure algebraic cycles; Chow group; motive; Bloch-Beilinson filtration; Beauville's ``splitting property'' conjecture; multiplicative Chow-Künneth decomposition; Fano varieties; tautological ring
0
zero cycles; Chow group of algebraic cycles; Hodge structure \(L\)-function; Shimura variety; Hilbert-Blumenthal surface; Tate's conjectures for abelian fields; group of algebraic cycles; intersection cohomology; canonical intermediate-perversity extension; Hirzebruch- Zagier cycles; Tate class Gordon, B. B.: Algebraic cycles in families of abelian varieties over Hilbert -- blumenthal surfaces. J. reine angew. Math. 449, 149-171 (1994)
0
zero cycles; Chow group of algebraic cycles; Hodge structure decomposition of diagonal; Calabi-Yau complete intersection; decomposable 0-cycle; Chow ring; intersection theory; Hodge structure Fu, L, Decomposition of small diagonals and Chow rings of hypersurfaces and Calabi-Yau complete intersections, Adv. Math., 244, 894-924, (2013)
0
zero cycles; Chow group of algebraic cycles; Hodge structure group of automorphisms of smooth curve; \(L\)-functions; zeta-functions; Galois covering; class numbers; varieties over finite fields; Betti numbers; rank of the Mordell-Weil group; conjectures of Birch-Swinnerton-Dyer; Tate conjectures on algebraic cycles Kani, No article title, J. Number Theory, 46, 230, (1994)
0
zero cycles; Chow group of algebraic cycles; Hodge structure number of rational points; homotopy type; Grassmann variety; Betti numbers; complex algebraic variety; mixed Hodge structure; weight filtration; Hodge filtration; invariant; weight polynomial; Euler characteristic
0
zero cycles; Chow group of algebraic cycles; Hodge structure Bloch's conjecture; Chow group; zero cycles
0
zero cycles; Chow group of algebraic cycles; Hodge structure fundamental group; crystalline cohomology; finite characteristic; algebraic K-theory; Hodge-Witt logarithmic cohomology; Chow group M. Gros, ''Sur la partie \(p\)-primaire du groupe de Chow de codimension deux,'' Comm. Algebra, vol. 13, iss. 11, pp. 2407-2420, 1985.
0
zero cycles; Chow group of algebraic cycles; Hodge structure Chow group; torsion zero-cycles; projective surface Masanori Asakura and Shuji Saito, Surfaces over a \?-adic field with infinite torsion in the Chow group of 0-cycles, Algebra Number Theory 1 (2007), no. 2, 163 -- 181.
0
zero cycles; Chow group of algebraic cycles; Hodge structure Gersten's conjecture; characteristic \(p\); finiteness of \(p\)-torsion of zero-cycles; purity theorems for logarithmic Hodge-Witt sheaves; Cousin complex N. Suwa, ''A note on Gersten's conjecture for logarithmic Hodge-Witt sheaves,'' \(K\)-Theory, vol. 9, iss. 3, pp. 245-271, 1995.
0
zero cycles; Chow group of algebraic cycles; Hodge structure zero cycles on singular varieties; infinite dimensionality; Chow groups; Albanese maps; algebraic cycles Srinivas, V., \textit{zero cycles on singular varieties}, The arithmetic and geometry of algebraic cycles, Banff, AB, 1998, 347-382, (2000), Kluwer Academic Publishers, Dordrecht
0
zero cycles; Chow group of algebraic cycles; Hodge structure Feynman integral; Feynman diagram; Tate motive; perturbative quantum field theory; period; oscillatory integral; Gelfand-Leray form; Connes-Kreimer theory; Radon transform; Hodge structure; noncommutative geometry; Galois group; supermanifold; Kirchhoff-Symaznik polynomial; dimensional regularization; BPHZ renormalization; Tannakian category; Grothendieck ring; monodromy; weight fibration; vanishing cycles; topological simplex; singularities; mixed Tate; tubular neighborhood; Kummer motive; Milnor fiber; motivic sheaves; normal crossings; Picard-Fuchs equation; Riemann-Hilbert correspondence; Hopf algebra; Igusa L-function Marcolli, M.: Feynman Motives. World Scientific, Singapore (2010)
0
zero cycles; Chow group of algebraic cycles; Hodge structure Galois module structure of the cohomology groups; finite étale Galois covering; fundamental group of an algebraic curve Nakajima, Shōichi: On Galois module structure of the cohomology groups of an algebraic variety. Invent. math. 75, No. 1, 1-8 (1984)
0
zero cycles; Chow group of algebraic cycles; Hodge structure Merkurev-Seislin theorem; Quillen-Lichtenbaum conjectures; algebraic K- theory of fields; Brauer-Severi varieties; Milnor K-groups; Bloch's group; Chow groups A. A. Suslin, ''Algebraic \(K\)-theory of fields,'' in Proceedings of the International Congress of Mathematicians, Vol. 1, 2, Providence, RI, 1987, pp. 222-244.
0
zero cycles; Chow group of algebraic cycles; Hodge structure variation of a Hodge structure; monodromy group Peters, C. A. M.; Steenbrink, J. H. M., Monodromy of variations of Hodge structure, Acta Applicandae Mathematicae, 75, 183-194, (2003)
0
zero cycles; Chow group of algebraic cycles; Hodge structure group schemes; arithmetic groundfields; degenerations of abelian varieties; arithmetic compactifications for the moduli spaces; principally polarized abelian varieties; geometric invariant theory; deformation theory; algebraization of formal moduli; Satake-Baily-Borel compactification; toroidal compactification; degenerations of polarized abelian varieties; polarizations; algebraic stack; Shimura varieties; equivariant sheaves; Hodge theory; De Rham cohomology; crystalline cohomology; action of Hecke operators; conformal quantum field theory G. \textsc{Faltings} and C.-L. \textsc{Chai}, \textit{Degeneration of Abelian Varieties}, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol.~22, Springer, Berlin, 1990, with an Appendix by David Mumford.
0
zero cycles; Chow group of algebraic cycles; Hodge structure algebraic cycles; \(p\)-adic étale cohomology; complete intersection; Chow group; coniveau filtration Spencer Bloch and Hélène Esnault, The coniveau filtration and non-divisibility for algebraic cycles, Math. Ann. 304 (1996), no. 2, 303 -- 314.
0
zero cycles; Chow group of algebraic cycles; Hodge structure torsion cycle map; Chow group of cycles of codimension two; Hochschild-Serre spectral sequence K. Sato, Injectivity of the torsion cycle map of codimension two of varieties over \(p\)-adic fields with semi-stable reduction , J. Reine Angew. Math. 501 (1998), 221--235.
0
zero cycles; Chow group of algebraic cycles; Hodge structure arrangement of hyperplanes; mixed Hodge structure on the fundamental group Kawahara, Y.: The mixed Hodge structure on the fundamental group of the fiber type 2-arrangement. Nagoya math. J. 147, 113-136 (1997)
0
zero cycles; Chow group of algebraic cycles; Hodge structure mixed Hodge structure; germ of holomorphic function; Grothendieck group; convolution theorem; non-degenerate with respect to Newton boundary; tame \(l\)-adic sheaves; composite singularities
0
zero cycles; Chow group of algebraic cycles; Hodge structure Hodge cohomology groups; infinite dimensionality of the Chow group V. Srinivas, Gysin maps and cycle classes in Hodge cohomology, Proc. Indian Acad. Sci. Math. Sci. 103 (1993), 209--247.
0
zero cycles; Chow group of algebraic cycles; Hodge structure Chow group; codimension two algebraic cycles; generic abelian variety M. V. Nori, ''Cycles on the generic abelian threefold,'' Proc. Indian Acad. Sci. Math. Sci., vol. 99, iss. 3, pp. 191-196, 1989.
0
zero cycles; Chow group of algebraic cycles; Hodge structure torsion subgroup of second Chow group; \(K_ 2\)-cohomology; Galois module structure; Bloch-Quillen-formula; Neron-Severi group; Picard variety Colliot-Thélène, J.-L. and Raskind, W.: K 2-Cohomology and the second Chow group, Math. Ann. 270 (1985), 165-199.
0
zero cycles; Chow group of algebraic cycles; Hodge structure étale homology theory; torsion part of the group of rational classes of zero-cycles S. Saito, ''Torsion zero-cycles and étale homology of singular schemes,'' Duke Math. J., vol. 64, iss. 1, pp. 71-83, 1991.
0
zero cycles; Chow group of algebraic cycles; Hodge structure algebraic cycles; moving lemma; higher Chow group; additive higher Chow group; linear projection; Grassmannian
0
zero cycles; Chow group of algebraic cycles; Hodge structure torsion group of Chow group; codimension two cycles; rational equivalence; modulo rational equivalence Jean-Louis Colliot-Thélène and Wayne Raskind, Groupe de Chow de codimension deux des variétés définies sur un corps de nombres: un théorème de finitude pour la torsion, Invent. Math. 105 (1991), no. 2, 221 -- 245 (French, with English summary).
0
zero cycles; Chow group of algebraic cycles; Hodge structure torsion zero cycles; Selmer group of the symmetric square; Hyodo-Kato cohomology; selfproduct of a semistable elliptic curve Andreas Langer, Selmer groups and torsion zero cycles on the selfproduct of a semistable elliptic curve, Doc. Math. 2 (1997), 47 -- 59.
0
zero cycles; Chow group of algebraic cycles; Hodge structure algebraic cycles; Chow groups; motives; Bloch's conjecture; Bloch-Beilinson filtration; hyperkähler varieties; \(K3\) surfaces; Hilbert schemes; non-symplectic involution; multiplicative Chow-Künneth decomposition; ``spread'' of algebraic cycles in a family
0
zero cycles; Chow group of algebraic cycles; Hodge structure algebraic theory of quadratic forms; Witt groups and rings; algebraic \(K\)-theory; algebraic cycles; Chow groups and rings; cohomology operations; motives; projective quadrics Elman, R.; Karpenko, N.; Merkurjev, A., \textit{The Algebraic and Geometric Theory of Quadratic Forms}, 56, (2008), Providence, RI
0
zero cycles; Chow group of algebraic cycles; Hodge structure Mumford-Tate group; period domain; variation of Hodge structure; Noether-Lefschetz locus Green, M; Griffiths, P; Kerr, M, Mumford-Tate domains, Boll. Unione Mat. Ital (9), 3, 281-307, (2010)
0
zero cycles; Chow group of algebraic cycles; Hodge structure algebraic cycles; Chow groups; motives; finite-dimensional motives; surfaces of general type; Todorov surfaces; \(K3\) surfaces R. Laterveer, Algebraic cycles and Todorov surfaces, to appear in Kyoto J. Math., arXiv:1609.09629.
0
zero cycles; Chow group of algebraic cycles; Hodge structure nilmanifolds; homotopy type of the classifying space of a finitely generated (torsion free) nilpotent group; links of isolated singularities; Heisenberg group; link of an isolated \(n\)-fold singularity; mixed Hodge structure Richard M. Hain, ``Nil-manifolds as links of isolated singularities'', Compos. Math.84 (1992) no. 1, p. 91-99
0
zero cycles; Chow group of algebraic cycles; Hodge structure Chow group; filtration; higher Abel-Jacobi map; algebraic cycles S. Saito, ``Motives, algebraic cycles and Hodge theory'' in The Arithmetic and Geometry of Algebraic Cycles (Banff, Alberta, 1998) , CRM Proc. Lecture Notes 24 , Amer. Math. Soc., Providence, 2000, 235--253.
0
zero cycles; Chow group of algebraic cycles; Hodge structure Noether-Lefschetz locus; infinitesimal variation of Hodge structures; algebraic cycles
0
zero cycles; Chow group of algebraic cycles; Hodge structure Abel's theorem; geometry of webs; algebraic cycles; chow groups; transcendental numbers Griffiths, P.; Laudal, O. A. (ed.); Piene, R. (ed.), The legacy of Abel in algebraic geometry, 179-205, (2004)
0
zero cycles; Chow group of algebraic cycles; Hodge structure arithmetic cycles; arithmetically ample line bundle; Chow group; Grothendieck's standard conjectures; regular arithmetic varieties; Hodge index theorem Moriwaki, A., \textit{Hodge index theorem for arithmetic cycles of codimension one}, Math. Res. Lett., 3, 173-183, (1996)
0
zero cycles; Chow group of algebraic cycles; Hodge structure algebraic cycles; arithmetic finiteness theorem; Galois cohomology; 0-dimensional Chow group; fibrations; Severi-Brauer variety Emmanuelle Frossard, Groupe de Chow de dimension zéro des fibrations en variétés de Severi-Brauer, Compositio Math. 110 (1998), no. 2, 187 -- 213 (French, with English summary).
0
zero cycles; Chow group of algebraic cycles; Hodge structure algebraic group; parabolic subgroup; Gysin homomorphism; Chow group; Todd class of the tangent bundle Michel Brion, The push-forward and Todd class of flag bundles, Parameter spaces (Warsaw, 1994) Banach Center Publ., vol. 36, Polish Acad. Sci. Inst. Math., Warsaw, 1996, pp. 45 -- 50.
0
zero cycles; Chow group of algebraic cycles; Hodge structure Witt group of skew-symmetric non-singular bilinear forms; real algebraic variety of dimension 4; ring of \({\mathbb{C}}\)-valued regular functions; Chow ring; algebraic hypersurfaces
0
zero cycles; Chow group of algebraic cycles; Hodge structure zero estimates of transcendence theory on a commutative algebraic group; periods; Abelian varieties; tori; Hilbert polynomials; Riemann-Roch theorem; lattices; Minkowski theorem Bertrand, D.; Philippon, P.: Sous-groupes algébriques de groupes algébriques commutatifs. Illinois J. Math. 32, 263-280 (1988)
0
zero cycles; Chow group of algebraic cycles; Hodge structure algebraic cycles; Chow groups; motives; Bloch's conjecture; Bloch-Beilinson filtration; hyperkähler varieties; Fano varieties of lines on cubic fourfolds; multiplicative Chow-Künneth decomposition; splitting property; finite-dimensional motive
0
zero cycles; Chow group of algebraic cycles; Hodge structure algebraic cycles; Chow groups; motives; Bloch -- Beilinson filtration; hyperkähler varieties; Fano variety of lines on cubic fourfold; Voisin's conjecture
0
zero cycles; Chow group of algebraic cycles; Hodge structure regular homomorphism; Chow group; algebraic cycles; intermediate Jacobian; Abel-Jacobi map Murre, JP, Un résultat en théorie des cycles algébriques de codimension deux, C. R. Acad. Sci. Paris, 296, 981-984, (1983)
0
zero cycles; Chow group of algebraic cycles; Hodge structure algebraic cycles; Chow groups; motives; Bloch conjecture; surfaces of general type; Voisin's ``spread'' method
0
zero cycles; Chow group of algebraic cycles; Hodge structure threefold; family of algebraic 1-cycles; Abel-Jacobi map; intermediate Jacobian; Grothendieck's generalized Hodge conjecture
0
zero cycles; Chow group of algebraic cycles; Hodge structure cohomology of complement of algebraic hypersurface; rational differential forms; jacobian ideal; Leray exact sequence; mixed Hodge structure
0
zero cycles; Chow group of algebraic cycles; Hodge structure algebraic cycles over finite fields; zeta function; Riemann-Roch; zeta functions of zero cycles Wan, D.: Zeta functions of algebraic cycles over finite fields. Manuscripta math. 74, 413-444 (1992)
0
zero cycles; Chow group of algebraic cycles; Hodge structure field of characteristic zero; integrable \(K\)-connection; smooth variety; characteristic classes; Chow group; cycle map in the Deligne cohomology Esnault, Hélène, Characteristic classes of flat bundles. II, \(K\)-Theory, 6, 1, 45-56, (1992)
0
zero cycles; Chow group of algebraic cycles; Hodge structure Hodge conjecture; algebraic cycles; Weil Hodge structure on abelian 4- folds with complex multiplication C. Schoen, Hodge classes on selfproducts of a variety with an automorphism,Compositio Math.65 (1988), 3--32.
0
zero cycles; Chow group of algebraic cycles; Hodge structure projective toric variety; one-parameter subgroup; wall-crossing; semi-orthogonal decomposition; singularity categories; full exceptional collection; GIT; windows; geometric invariant theory; fan structure; bounded derived category of coherent sheaves; equivariant ample line bundle; VGIT; reductive linear algebraic group; variations of GIT structures; birational methods; blow-ups at smooth centres; linearisation of a group action
0
zero cycles; Chow group of algebraic cycles; Hodge structure embeddings of the algebraic homogeneous space; Demazure embedding; mangificent embedding; spherical algebraic homogeneous space; weights; orbit structure; quotients; root system; Weyl group Brion, Michel, Vers une généralisation des espaces symétriques, J. Algebra, 134, 1, 115-143, (1990)
0
zero cycles; Chow group of algebraic cycles; Hodge structure quadratic forms; Pfister forms; Witt ring; function field of a quadric; generic splitting; Brauer group; Brauer-Wall group; index reduction; Galois cohomology; Milnor \(K\)-theory; Milnor conjecture; unramified Witt ring; unramified cohomology; algebraic cycles; Rost motive; motivic decomposition; Steenrod operations Kahn, B.: Formes Quadratiques sur un Corps. Société Mathématique de France, Paris (2008)
0
zero cycles; Chow group of algebraic cycles; Hodge structure Dedekind ring; central simple algebra; hereditary R-order; Grothendieck group; finitely generated locally free \(\Lambda\)-modules; class group; finiteness theorems; affine k-algebra; Chow group; 0-dimensional cycles; conic bundle surface; sheaves of orders; Galois cohomology; global sections; Quillen resolution; Severi-Brauer schemes; reduced norm; Merkur'ev-Suslin theorems; cup-product; coordinate ring; smooth affine curve Salberger, P.:K-theory of orders and their Brauer-Severi schemes. Thesis, Department of Mathematics, University of G?teborg 1985
0
zero cycles; Chow group of algebraic cycles; Hodge structure Chow group; algebraic cycle; regulator; Beilinson-Hodge conjecture; Abel-Jacobi map; Bloch-Beilinson filtration
0
zero cycles; Chow group of algebraic cycles; Hodge structure discrete group; Chow ring valued characteristic classes for algebraic bundles; complex representation; multiplicative transfer; Chern classes of the induced representation; Riemann-Roch formula for induced representations; Stiefel-Whitney classes of real representations Fulton, W., MacPherson, R.: Characteristic classes of direct image bundles for covering maps. Ann. Math. (2) 125, 1--92 (1987)
0
zero cycles; Chow group of algebraic cycles; Hodge structure category of motives; envelope of schemes; Chow groups; Quillen's \(K\)-theory; homotopy limits; smooth projective varieties; algebraic cycles; hyperenvelope; simplicial schemes; Grothendieck topology; weight complex; canonical triangle; product formula; Gersten complexes of schemes; homotopy equivalence; Tate motive; blow-up; pairings Gillet, H; Soulé, C, Descent, motives and K-theory, Crelle J. Reine Angew. Math., 478, 127-176, (1996)
0
zero cycles; Chow group of algebraic cycles; Hodge structure Hodge structure; Gauss-Manin connection; periods of tame polynomials; Fermat varieties; vanishing cycles; Brieskorn module
0
zero cycles; Chow group of algebraic cycles; Hodge structure linear algebraic groups; pseudo-reductive groups; generalized standard construction; groups locally of minimal type; structure and classification of pseudo-reductive groups; imperfect fields; pseudo-split groups; central extensions; affine group schemes Conrad, B.; Prasad, G., Classification of pseudo-reductive groups, Annals of Mathematics Studies, (2015), Princeton University Press
0
zero cycles; Chow group of algebraic cycles; Hodge structure multiplicative structure; division algebras over number fields; reduced norm; group of rational points; anisotropic algebraic group; maximal cyclic subfield; SL(1,D); Hasse norm principle; central simple skew field
0
zero cycles; Chow group of algebraic cycles; Hodge structure hyper-Kähler varieties; Lagrangian subvarieties; Fano variety of lines; algebraic cycles; Chow rings
0