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

Access to Document

10.1016/j.jnt.2004.04.006

Cite this

@article{4ae9d80f0f994bfcb18f3debdc867eaa,

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: zarhin@math.psu.edu.",

year = "2004",

month = sep,

doi = "10.1016/j.jnt.2004.04.006",

language = "English (US)",

volume = "108",

pages = "44--59",

journal = "Journal of Number Theory",

issn = "0022-314X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - The Tate conjecture for powers of ordinary cubic fourfolds over finite fields

AU - Zarhin, Y. G.

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: zarhin@math.psu.edu.

PY - 2004/9

Y1 - 2004/9

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.

UR - http://www.scopus.com/inward/record.url?scp=4344586993&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4344586993&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2004.04.006

DO - 10.1016/j.jnt.2004.04.006

M3 - Article

AN - SCOPUS:4344586993

VL - 108

SP - 44

EP - 59

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 1

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this