**ODTÜ-BİLKENT
ALGEBRAIC**** GEOMETRY SEM****I****NAR**

**“Trivial Zeros, Kolyvagin Systems and Main Conjectures of
Iwasawa Theory”**

by

**Kazım
Büyükboduk**

** **

** **

**Abstract:** Kolyvagin's
machinery of Euler Systems is a powerful tool used to bound
Selmer groups. If one looks at the Selmer groups over the Iwasawa tower,

same methods are used to prove that the characterictic ideal of the Selmer

group divides the ideal generated by the associated p-adic L-function (Main

conjectures in various settings state that these ideals in fact coincide).

Mazur and Rubin isolated the notion of "Kolyvagin System", which have

exactly the same applications as Euler Systems, but have a more rigid

structure. We prove that Kolyvagin Systems over the Iwasawa tower exist as

long as a certain trivial zero phenomenon does not
occur.

**Date:** 30
December, 2005 Friday

**Time:** 14:40

**Place:** Bilkent, Mathematics Seminar Room
SA-141

** **

**Tea and cookies will
be served before the talk.**