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Mathematics and Computer Sciences

Seminars

Year : Project :

Next seminars

lundi 8 mars 2010 (tn)

Fonction rayon de convergence : un exemple éclairant

Gilles Christol (Paris)

Abstract

lundi 22 mars 2010 (tn)

On the Z_p-ranks of tamely ramified Iwasawa modules

Manabu Ozaki (Osaka)

Abstract

This talk is based on a joint work with Y.Mizusawa
and T.Itoh. 
For a number field $k$, a prime number $p$,
and a finite set $S$ of prime numbers with $p\not\in S$, 
we let $X_S(k_\infty)$ be the Galois group
of the maximal $S$-ramified abelian $p$-extension
over the cyclotomic $\mathbb{Z}_p$-extension field $k_\infty$
of $k$. 
In this talk, I will give a formula for
the $\mathbb{Z}_p$-rank of $X_S(\mathbb{Q}_\infty)$.
In the case where $p=2$ and $k$ is an imaginary quadratic field,
I will also give a formulae, which is regarded as
a tamely ramified version of Kida's formula.