TATE CLASSES ON SELF-PRODUCTS OF ABELIAN VARIETIES OVER FINITE FIELDS

Yuri G. Zarhin

doi:10.5802/aif.3483

TATE CLASSES ON SELF-PRODUCTS OF ABELIAN VARIETIES OVER FINITE FIELDS

Yuri G. Zarhin

Mathematics

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

1 Scopus citations

Abstract

We deal with g-dimensional abelian varieties X over finite fields. We prove that there is a universal constant (positive integer) N = N(g) that depends only on g that enjoys the following property. If a certain self-product of X carries an exotic Tate class then the self-product X^2N of X also carries an exotic Tate class. This gives a positive answer to a question of Kiran Kedlaya.

Original language	English (US)
Pages (from-to)	2339-2383
Number of pages	45
Journal	Annales de l'Institut Fourier
Volume	72
Issue number	6
DOIs	https://doi.org/10.5802/aif.3483
State	Published - 2022

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Geometry and Topology

Access to Document

10.5802/aif.3483

Cite this

@article{ae737587bddd4a93b358e10e6bf7f24d,

title = "TATE CLASSES ON SELF-PRODUCTS OF ABELIAN VARIETIES OVER FINITE FIELDS",

abstract = "We deal with g-dimensional abelian varieties X over finite fields. We prove that there is a universal constant (positive integer) N = N(g) that depends only on g that enjoys the following property. If a certain self-product of X carries an exotic Tate class then the self-product X2N of X also carries an exotic Tate class. This gives a positive answer to a question of Kiran Kedlaya.",

author = "Zarhin, {Yuri G.}",

year = "2022",

doi = "10.5802/aif.3483",

language = "English (US)",

volume = "72",

pages = "2339--2383",

journal = "Annales de l'Institut Fourier",

issn = "0373-0956",

publisher = "Association des Annales de l'Institut Fourier",

number = "6",

}

TY - JOUR

T1 - TATE CLASSES ON SELF-PRODUCTS OF ABELIAN VARIETIES OVER FINITE FIELDS

AU - Zarhin, Yuri G.

PY - 2022

Y1 - 2022

N2 - We deal with g-dimensional abelian varieties X over finite fields. We prove that there is a universal constant (positive integer) N = N(g) that depends only on g that enjoys the following property. If a certain self-product of X carries an exotic Tate class then the self-product X2N of X also carries an exotic Tate class. This gives a positive answer to a question of Kiran Kedlaya.

AB - We deal with g-dimensional abelian varieties X over finite fields. We prove that there is a universal constant (positive integer) N = N(g) that depends only on g that enjoys the following property. If a certain self-product of X carries an exotic Tate class then the self-product X2N of X also carries an exotic Tate class. This gives a positive answer to a question of Kiran Kedlaya.

UR - http://www.scopus.com/inward/record.url?scp=85137784388&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85137784388&partnerID=8YFLogxK

U2 - 10.5802/aif.3483

DO - 10.5802/aif.3483

M3 - Article

AN - SCOPUS:85137784388

SN - 0373-0956

VL - 72

SP - 2339

EP - 2383

JO - Annales de l'Institut Fourier

JF - Annales de l'Institut Fourier

IS - 6

ER -

TATE CLASSES ON SELF-PRODUCTS OF ABELIAN VARIETIES OVER FINITE FIELDS

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this