Rigid inner forms of real and p-adic groups

By Tasho Kaletha. 2013

78 citations recorded by the source corpus.

We define a new cohomology set for an affine algebraic group G and a multiplicative 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 normalize the Langlands-Shelstad endoscopic transfer factors and to give a conjectural description of the internal structure and endoscopic transfer of L-packets for arbitrary connected reductive groups that extends the well-known conjectural description for quasi-split groups. In the real case, we show that this description is correct using Shelstad's work.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/83d4f1adf0d99e418b24d4d7daaefa77385e39a9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. M. Solleveld
2. Tasho Kaletha
3. Jessica Fintzen
4. Mark Reeder
5. J. Yu

In Mathematical Physics

1. P. Baum
2. Anne-Marie Aubert
3. M. Solleveld
4. Tasho Kaletha
5. Jessica Fintzen
6. Guoliang Yu
7. N. Higson
8. J. Roe

Citations in the corpus

• Regular supercuspidal representations (2016, methodology): “mbeddings of Sinto G. The internal parameterization of this L-packet is again done as in [Kal15, §4.3], the only difference being that now we are using the cohomology functor H1(u→ W,−) introduced in [Kala] instead of the set B(G) bas used in [Kal15]. This allows us to uniformly treat all connected ”
• The local Langlands correspondence for inner forms of SL$$_{n}$$n (2013, background): “It is worth noting that our group C(φ ) coincides with the group S+ φ defined by Kaletha in [32] with Z taken to be equal to the centre of SLn(F ).”