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Izv. RAN. Ser. Mat., 1999, Volume 63, Issue 6, Pages 167–208 (Mi izv272)  

Cycles of small codimension on a simple $2p$- or $4p$-dimensional Abelian variety

S. G. Tankeev

Vladimir State University

Abstract: Let $J$ be a simple $2p$- or $4p$-dimensional Abelian variety over the field of complex numbers, where $p\ne 5$ is a prime number. Assume that one of the following conditions holds:
1) $\operatorname{Cent End}^0(J)$ is a totally real field of degree 1, 2 or 4 over $\mathbb Q$;
2) $J$ is a simple $2p$-dimensional Abelian variety of CM-type $(K,\Phi)$ such that $K/\mathbb Q$ is a normal extension;
3) $J$ is a simple $2p$-dimensional Abelian variety such that $\operatorname{End}^0(J)$ is an imaginary quadratic extension of $\mathbb Q$.
Then for every positive integer $r<p$ the $\mathbb Q$-space $H^{2r}(J,\mathbb Q)\cap H^{r,r}$ is spanned by cohomology classes of intersections of divisors.

DOI: https://doi.org/10.4213/im272

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English version:
Izvestiya: Mathematics, 1999, 63:6, 1221–1262

Bibliographic databases:

MSC: 14K05, 14C30
Received: 10.02.1998

Citation: S. G. Tankeev, “Cycles of small codimension on a simple $2p$- or $4p$-dimensional Abelian variety”, Izv. RAN. Ser. Mat., 63:6 (1999), 167–208; Izv. Math., 63:6 (1999), 1221–1262

Citation in format AMSBIB
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