The Kottwitz conjecture describes the cohomology of basic Rapoport–Zink spaces using local Langlands correspondences. In this paper, via geometrical studies some Kottwitz-type Shimura varieties, we prove for simple unramified unitary PEL type signature (1,n-1).

Smooth irreducible representations of tori over local fields have been parameterized by Langlands, using class field theory and Galois cohomology. This paper extends this parameterization to central extensions of such tori, which arise naturally in the setting of nonlinear covers of reductive groups.

1.1. The case ` 6= p. In this case, we are in the setting of the classical Local Langlands Correspondence, which can be stated (roughly) as follows: Let n ≥ 1. We then have an injective map (1)  continuous representations of Gal(Qp/Qp) on n-dimensional Q`-vector spaces, up to isomorphism  ↪−→  irreducible, admissible representations of GLn(Qp) on Q`-vector spaces, up to isomor...

We describe in brief some aspects of the Langlands program, focussing on Euler products, and also some new constructions, where Euler products are replaced by twisted Euler products. The twisted Euler products are related to automorphic forms on metaplectic groups. 2000 Mathematics Subject Classification: 11F66, 11F55, 11F70, 11M41, 22E55.

The main objective consists in endowing the elementary particles with an algebraic space-time structure in the perspective of unifying quantum field theory and general relativity: this is realized in the frame of the Langlands global program based on the infinite dimensional representations of algebraic groups over adele rings. In this context, algebraic quanta, strings and fields of particles ...

We formulate a version of the Breuil–Mézard conjecture for quaternion algebras, and show that it follows from the Breuil–Mézard conjecture for GL2. In the course of the proof we establish a mod p analogue of the Jacquet– Langlands correspondence for representations of GL2(k), k a finite field of characteristic p.

By applying the residue method for period integrals, we prove identities between integrals on cuspidal automorphic representations and residual seven spherical varieties. Combining this with Langlands–Shahidi theory residues of Eisenstein series, each case, some relations certain L-functions. In cases, also study local multiplicity