Rigid inner forms of real and p-adic groups

Abstract

We dene a new cohomology set H 1 (u ! W;Z ! G) for an ane algebraic group G and a nite central subgroup, both dened over a local eld of characteristic zero, which is an enlargement of the usual rst Galois cohomology set of G. We show how this set can be used to give a precise conjectural description of the internal structure and endoscopic transfer of tempered L-packets for arbitrary connected reductive groups that extends the well-known conjectural description for quasi-split groups. In the case of real groups, we show that this description is correct using Shelstad’s work.