Seminar on Arithmetic Algebraic Geometry: Birch and Swinnerton-Dyer conjecture (1)

2010-12-23 10:00 - 2010-12-23 12:00
Faculty of Science Building #3 Room 413
Fabien Trihan(University of Nottingham)
The Birch and Swinnerton-Dyer conjecture relates arithmetic data associated to an elliptic curve E over a global field K to the behaviour of the Hasse-weil L-function L(E, s) of E at s = 1. More specifically, it is conjectured that the rank of the abelian group E(K) of points of E is the order of the zero of L(E, s) at s = 1, and the first non-zero coefficient in the Taylor expansion of L(E, s) at s = 1 is given by more refined arithmetic data attached to E over K.
We plan to give a lecture on what is known in the case where the field K is a function field of characteristic p>0.