Conference "Zeta Functions"

Special values of L-functions and Iwasawa’s theory

Vésale Nicolas (Besançon)

Friday 25 June, 18:00 - 19:00

Abstract

Let K/k be an abelian extension of number fields with Galois group G. Let O_K be the ring of integers of K. The study the Z[G]-structure of the K- groups Km(O_K) naturally begins with the computation of their annihilators. Following Iwasawa’s theory, such computations for K-groups can be recasted in terms of special values of zeta functions. Snaith recently gave a generalization of this result in the case when G is no more trivial. Using special values of L-functions, he built an ideal J_K=k(m), and proposed a conjecture (for p odd). In the same paper, he proved the conjecture when m is not zero and K is a cyclotomic field. In this talk, we will explain how Iwasawa’s theory can be used to prove these results.