Tom Weston (University of Michigan)

The Selmer group of a Galois representation is a certain Galois

cohomology group which is conjeturally related to special values

of L-functions, generalizing the usual Selmer group of an abelian

variety and the conjecture of Birch and Swinnerton-Dyer. I will

define geometric Euler systems and explain how they yield

annihilators for Selmer groups. I will attempt to explain the

differences with the arithmetic approach of Kolyvagin, Rubin and

others; the geometric theory is vastly simpler but also somewhat

less effective. I will then explain how one can use algebraic

cycles to produce geometric Euler systems in the cohomology of

algebraic varieties. I will conclude with some examples from

the theory of modular forms.