The Tate conjecture for powers of ordinary cubic fourfolds over finite fields

Y. G. Zarhin

doi:10.1016/j.jnt.2004.04.006

The Tate conjecture for powers of ordinary cubic fourfolds over finite fields

Y. G. Zarhin

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Recently, Levin proved the Tate conjecture for ordinary cubic fourfolds over finite fields. In this paper, we prove the Tate conjecture for self-products of ordinary cubic fourfolds. Our proof is based on properties of so-called polynomials of K3-type introduced by the author about 12 years ago.

Original language	English (US)
Pages (from-to)	44-59
Number of pages	16
Journal	Journal of Number Theory
Volume	108
Issue number	1
DOIs	https://doi.org/10.1016/j.jnt.2004.04.006
State	Published - Sep 2004

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jnt.2004.04.006

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title = "The Tate conjecture for powers of ordinary cubic fourfolds over finite fields",

abstract = "Recently, Levin proved the Tate conjecture for ordinary cubic fourfolds over finite fields. In this paper, we prove the Tate conjecture for self-products of ordinary cubic fourfolds. Our proof is based on properties of so-called polynomials of K3-type introduced by the author about 12 years ago.",

author = "Zarhin, \{Y. G.\}",

note = "Funding Information: \$Partially supported by the NSF. ·Department of Mathematics, Eberly College of Science, The Pennsylvania State University, Room 325, McAllister Building, University Park, PA 16802, USA. E-mail address: [email protected].",

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N1 - Funding Information: $Partially supported by the NSF. ·Department of Mathematics, Eberly College of Science, The Pennsylvania State University, Room 325, McAllister Building, University Park, PA 16802, USA. E-mail address: [email protected].

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N2 - Recently, Levin proved the Tate conjecture for ordinary cubic fourfolds over finite fields. In this paper, we prove the Tate conjecture for self-products of ordinary cubic fourfolds. Our proof is based on properties of so-called polynomials of K3-type introduced by the author about 12 years ago.

AB - Recently, Levin proved the Tate conjecture for ordinary cubic fourfolds over finite fields. In this paper, we prove the Tate conjecture for self-products of ordinary cubic fourfolds. Our proof is based on properties of so-called polynomials of K3-type introduced by the author about 12 years ago.

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The Tate conjecture for powers of ordinary cubic fourfolds over finite fields

Abstract

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