Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals → CJM
Abstract view

# Tate Cycles on Abelian Varieties with Complex Multiplication

Published:2014-03-18
Printed: Feb 2015
• V. Kumar Murty,
Department of Mathematics, University of Toronto, 40 St. George St., Toronto, CANADA M5S 2E4
• Vijay M. Patankar,
Indian Statistical Instiute, Chennai, India, 600113
 Format: LaTeX MathJax PDF

## Abstract

We consider Tate cycles on an Abelian variety $A$ defined over a sufficiently large number field $K$ and having complex multiplication. We show that there is an effective bound $C = C(A,K)$ so that to check whether a given cohomology class is a Tate class on $A$, it suffices to check the action of Frobenius elements at primes $v$ of norm $\leq C$. We also show that for a set of primes $v$ of $K$ of density $1$, the space of Tate cycles on the special fibre $A_v$ of the Néron model of $A$ is isomorphic to the space of Tate cycles on $A$ itself.
 Keywords: Abelian varieties, complex multiplication, Tate cycles
 MSC Classifications: 11G10 - Abelian varieties of dimension $> 1$ [See also 14Kxx] 14K22 - Complex multiplication [See also 11G15]

 top of page | contact us | privacy | site map |

© Canadian Mathematical Society, 2016 : https://cms.math.ca/