ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

4. Algebraic Geometry

1991 MS Classification: 14, 32 Tankeev, Serguei, Vladimir State University, Russia Algebraic cycles of small codimension on simple 2p- or 4pdimensional abelian variety Let J be a simple 2p- or 4p-dimensional abelian variety over the field of complex numbers, where p is a prime number. Assume that one of the following conditions holds: 1) Cent End^{0}(J) is a totally real field of degree 1,2,4 over ℚ ; 2) J is a simple 2p-dimensional abelian variety of CM-type (K, Φ) such that K/ℚ is a normal extension; 3) J is a simple 2p-dimensional abelian variety such that End^{0}(J) is an imaginary quadratic extension of ℚ. If p ≠ 5, then for all natural r < p the ℚ-space H^{2r}(J, ℚ) ∩ H^{r,r} is spanned by cohomology classes of intersections of divisors. If p ≠ 2, then H^{4}(J, ℚ) ∩ H^{2,2} is spanned by classes of intersections of divisors.