Elliptic p-units

par Werner Bley (LMU München)

mardi 9 oct. 2018, 10:45 → 11:45 Europe/Paris

Bât. Braconnier, salle Séminaire 1 (sous-sol) (ICJ, Université Lyon 1)

Let L/k be a finite abelian extension of an imaginary quadratic number field k. Let p be a rational prime which does not split in k/Q and let p denote the prime of O k lying over p. We assume that p splits completely in L/k. We then generalize a construction of Solomon and obtain in this way a pair of elliptic p-units in L. 

We then express their valuations in terms of a p-adic logarithm of an explicit elliptic unit generalizing a result of Solomon in the cyclotomic sitting. Results of this kind have applications in proofs of the equivariant Tamagawa number conjecture.

This is a report on joint work with Martin Hofer.