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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Pure Maths Colloquium: The Iwasawa $\mu$ invariant for degenerate Galois representations

Presented by Malte Witte, Paderborn

30 March 2015 16:00 in CM221

Let $e_n$ be the exponent of $p$ in the prime factorisation of the $n$-th layer of the cyclotomic $\mathbb{Z}_p$-extension of a number field $K$. A famous conjecture of Iwasawa predicts that the asymptotic growth of $e_n$ is linear in $n$, in other words, the Iwasawa $\mu$ invariant of $K$ vanishes. If $K$ is a Galois $p$-extension of an absolutely abelian number field, this is a well-known theorem. It seems to be less well-known that one can prove the conjecture also for number fields satisfying a certain condition on the Galois cohomology of the $p$-th roots of unity. The same condition may also be formulated for other Galois representations. For example, one thus obtains a sufficient condition for the strict Selmer group of an elliptic curve to have vanishing $\mu$-invariant, as predicted by Coates' and Sujatha's Conjecture A.

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