Rigid inner forms of real and $p$-adic groups

Tasho Kaletha

doi:10.4007/annals.2016.184.2.6

Geodesic

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Rigid inner forms of real and $p$-adic groups

Tasho Kaletha ¹

¹ Princeton University, Princeton, NJ

Annals of mathematics, Tome 184 (2016) no. 2, pp. 559-632.

Voir la notice de l'article provenant de la source Annals of Mathematics website

Résumé

We define a new cohomology set $H^1(u \to W,Z \to G)$ for an affine algebraic group $G$ and a finite central subgroup $Z$, both defined over a local field of characteristic zero, which is an enlargement of the usual first 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.

MR Zbl

DOI : 10.4007/annals.2016.184.2.6

Affiliations des auteurs :

Tasho Kaletha ¹

¹ Princeton University, Princeton, NJ

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Tasho Kaletha. Rigid inner forms of real and $p$-adic groups. Annals of mathematics, Tome 184 (2016) no. 2, pp. 559-632. doi : 10.4007/annals.2016.184.2.6. http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.184.2.6/

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