School of Physical Sciences
Jawaharlal Nehru University, New Delhi
Title : Tate's conjecture and poles of L-functions
Speaker: Prof. V. Kumar Murty
(University of Toronto, Canada)
Date: 30– July -2018
Time: 4 p.m, Monday
Venue: Seminar Room, SPS
Abstract : For a smooth projective variety X defined over a number field K, there are Lfunctions Lk(s) associated with the k-th l-adic cohomology space of X (more precisely of its base change to an algebraic closure of K). When k is even, Tate's conjecture predicts that Lk(s) has a pole at the real point of the edge of the critical strip of order equal to the dimension of the space of cycles on X of co dimension k/2 (modulo homological equivalence). In particular, this conjecture predicts that as we base change X to finite extensions of K, the order of pole should stabilize. In this talk, we shall discuss how this consequence can in fact be proved. We will give sufficient background to make the talk accessible to a general mathematical audience.