Seminar on Arithmetic Algebraic Geometry: Birch and SwinnertonDyer conjecture (1)
 Date

20101223 10:00 
20101223 12:00
 Place
 Faculty of Science Building #3 Room 413

Speaker/Organizer
 Fabien Trihan（University of Nottingham)

 The Birch and SwinnertonDyer conjecture relates arithmetic data associated to an elliptic curve E over a global field K to the behaviour of the Hasseweil Lfunction 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 nonzero 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.
http://www.math.sci.hokudai.ac.jp/~nakamura/index.html