Étale cohomology, cofinite generation, and p-adic L-functions

R.M.H. de Jeu, T.V. Navilarekallu

Research output: Contribution to JournalArticleAcademicpeer-review


Let p be a prime number. We study certain étale cohomology groups with coefficients associated to a p-adic Artin representation of the Galois group of a number field k. These coefficients are equipped with a modified Tate twist involving a p-adic index. The groups are cofinitely generated, and we determine the additive Euler characteristic. If k is totally real and the representation is even, we study the relation between the behaviour or the value of the p-adic L-function at the point e in its domain, and the cohomology groups with p-adic twist 1-e. In certain cases this gives short proofs of a conjecture by Coates and Lichtenbaum, and the equivariant Tamagawa number conjecture for classical L-functions. For p=2 our results involving p-adic L-functions depend on a conjecture in Iwasawa theory.
Original languageEnglish
Pages (from-to)2331-2383
Number of pages53
JournalAnnales de l'Institut Fourier
Issue number6
Publication statusPublished - 2015


Dive into the research topics of 'Étale cohomology, cofinite generation, and p-adic L-functions'. Together they form a unique fingerprint.

Cite this