# Thursday 08 Mar 2018: Elliptic p-units and the equivariant Tamagawa Number Conjecture

### Martin Hofer - Mathematisches Institut der Universitat Munchen

**H103** 14:30-16:30

The motivation for the main result presented in this talk comes from the study of the equivariant Tamagawa Number Conjecture(eTNC) for abelian extensions over an imaginary quadratic field k.

Bley proved the p-part of the eTNC for abelian extensions over k for odd primes p which split in k and do not divide the class number of k by adapting the proof of Burns and Greither for absolute abelian extensions. One key ingredient of both proofs is a construction of certain p-units and the computation of their valuation. In this talk I will now present a theorem (which is joint work with W. Bley) for the case where p is non-split in k. This case is traditionally more complicated because then we have to deal with a rank two Iwasawa algebra. The essential input for the proof is a computation of the constant term of a Coleman power series, where we use a recent result of T. Seiriki.