Chennai Mathematical Institute


3:30 pm, Seminar Hall
On Frobenius conjugacy class of some algebraic varieties over number fields

Abhijit Laskar
University of Regensburg, Germany.


For a smooth projective algebraic variety X defined over a number field F, the action of the absolute Galois group G of F on the absolute l-adic cohomology groups of X, induces certain representations of G. These Galois representations are one of the most extensively studied objects in Arithmetic Geometry and are subject to various famous conjectures. In this talk, we'll try to understand some of these conjectures (due to Deligne, Fontaine, Serre and Tate), using the base case of elliptic curves, which is relatively simpler to formulate. We'll also look at some partial results obtained in direction of these conjectures.

The talk will be accessible to non-specialists.