Hodge classes on self-products of a variety with an automorphism
Compositio Mathematica, Volume 65 (1988) no. 1, pp. 3-32.
@article{CM_1988__65_1_3_0,
     author = {Schoen, Chad},
     title = {Hodge classes on self-products of a variety with an automorphism},
     journal = {Compositio Mathematica},
     pages = {3--32},
     publisher = {Kluwer Academic Publishers},
     volume = {65},
     number = {1},
     year = {1988},
     zbl = {0663.14006},
     mrnumber = {930145},
     language = {en},
     url = {http://www.numdam.org/item/CM_1988__65_1_3_0/}
}
TY  - JOUR
AU  - Schoen, Chad
TI  - Hodge classes on self-products of a variety with an automorphism
JO  - Compositio Mathematica
PY  - 1988
DA  - 1988///
SP  - 3
EP  - 32
VL  - 65
IS  - 1
PB  - Kluwer Academic Publishers
UR  - http://www.numdam.org/item/CM_1988__65_1_3_0/
UR  - https://zbmath.org/?q=an%3A0663.14006
UR  - https://www.ams.org/mathscinet-getitem?mr=930145
LA  - en
ID  - CM_1988__65_1_3_0
ER  - 
%0 Journal Article
%A Schoen, Chad
%T Hodge classes on self-products of a variety with an automorphism
%J Compositio Mathematica
%D 1988
%P 3-32
%V 65
%N 1
%I Kluwer Academic Publishers
%G en
%F CM_1988__65_1_3_0
Schoen, Chad. Hodge classes on self-products of a variety with an automorphism. Compositio Mathematica, Volume 65 (1988) no. 1, pp. 3-32. http://www.numdam.org/item/CM_1988__65_1_3_0/

[A] Aoki, N., On some arithmetic problems related to the Hodge cycles on the Fermat varieties, Math. Ann. 266 (1983) 23-54. | MR | Zbl

[A-B] Atiyah, M.F. and Bott, R., A Lefschetz fixed point formula for elliptic differential operators, Bull. of the A.M.S. 72 (1966) 245-250. | MR | Zbl

[A-C-G-H] Arbarello, E. et al., Geometry of Algebraic Curves, Vol. 1, Grundlehren der math. Wissenschaften 267, Springer, New York (1985). | Zbl

[B] Beauville, A., Variétés de Prym et Jacobiennes Intermédiares, Ann. Scient. Éc. Norm. Sup., 4e serie, t. 10 (1977) 309-391. | Numdam | MR | Zbl

[B-S] Bloch, S. and Srinivas, V., Remarks on correspondences and algebraic cycles, Amer. J. of Math. 105 (1983) 1235-1254. | MR | Zbl

[B-T] Bott, R. and Tu, L., Differential Forms in Algebraic Topology. Springer, New York (1982). | MR | Zbl

[C-M] Conte, A. and Murre, J.P., The Hodge conjecture for fourfolds admitting a covering by rational curves, Math. Ann. 238 (1978) 79-88. | MR | Zbl

[D-M] Deligne, P., Hodge cycles on Abelian varieties, Notes by J.S. Milne, in " Hodge cycles, Motives, and Shimura varieties ", Lect. Notes in Math., 900, Springer (1982). | Zbl

[F] Fulton, W., Rational equivalence on singular varieties, Publ. Math. I.H.E.S. 45 (1975) 147-167. | Numdam | MR | Zbl

[G] Gross, B., On the periods of Abelian integrals and a formula of Chowla and Selberg, Invent. Math. 45 (1978) 193-211. | MR | Zbl

[G-H] Griffiths, P. and Harris, J., Principles of Algebraic Geometry. John Wiley and Sons, New York (1978). | MR | Zbl

[Gi] Gilkey, P., Lefschetz fixed point formulas and the heat equation, in Partial differential equations and geometry, Proceedings of the Park City Conference, ed. C. Byrnes, Marcel Dekker Lecture Notes in Pure and Applied Mathematics 48 (1979) 91-147. | MR | Zbl

[H] Hodge, W.V.D., The topological invariants of algebraic varieties, Proc. Int. Cong. Math. 182-192 (1950). | MR | Zbl

[H-Z] Hirzebruch, F. and Zagier, D., The Atiyah-Singer Theorem and Elementary Number Theory. Publish or Perish, Boston (1974). | MR | Zbl

[K] Kleiman, S.L., Algebraic cycles and the Weil conjectures, in Dix Exposés sur la Cohomologie des Schémas, North-Holland, Amsterdam, 359-386 (1968). | MR | Zbl

[M] Murty, V.K., Exceptional Hodge classes on certain Abelian varieties, Math. Ann. 268 (1984) 197-206. | MR | Zbl

[O] Oort, F., Finite group schemes, local moduli for Abelian varieties, and lifting problems, in Algebraic Geometry, Oslo 1970 (F. Oort, ed.), Wolters-Noordhoff, 233-254 (1972). | Zbl

[R] Ran, Z., Cycles on Fermat hypersurfaces, Compositio Math. 42 (1980) 121-142. | Numdam | MR | Zbl

[Ri] Ribet, K., Hodge classes on certain types of Abelian varieties, Am. J. Math. 105 (1983) 523-538. | MR | Zbl

[S] Shioda, T., The Hodge conjecture for Fermat varieties, Math. Ann. 245 (1979) 175-184. | MR | Zbl

[S2] Shioda, T., Algebraic Cycles on Abelian varieties of Fermat type, Math. Ann. 258 (1981) 65-80. | MR | Zbl

[S3] Shioda, T., What is known about the Hodge conjecture?, in Advanced Studies in Pure Mathematics 1, Algebraic Varieties and Analytic Varities, 55-68 (1983). | MR | Zbl

[SGA6] Berthelot, P., Grothendieck, A., Illusie, L., et al., Théorie des Intersections et Théoreme de Riemann-Roch, SGA 6 1966/67, Springer Lecture Notes 225 (1971). | MR | Zbl

[Sh] Shimura, G., On analytic families of polarized Abelian varieties and automorphic functions, Ann. of Math. 78 (1963) 149-192. | MR | Zbl

[St] Steenbrink, J.H.M., Mixed Hodge structure on the vanishing cohomology, in Real and Complex Singularities, Oslo 1976, P. Holm (ed.), Sijthoff and Noordhoff, 525-563 (1977). | MR | Zbl

[W] Weil, A., Abelian varieties and the Hodge ring, in Collected Papers III, (1979) 421-429.