In this paper, we prove that there is at most one correspondence between parahoric-spherical representations and semisimple local Langlands parameters which satisfies certain natural properties. Our proof of uniqueness statement very formal. particular, the constructed by Fargues Scholze yield unique candidate for such representations. As a corollary, conjecture posits compatibility with paraho...

Let G be a complex symplectic group. In [K1], we singled out the nilpotent cone N of some reducible G-module, which we call the (1-) exotic nilpotent cone. In this paper, we study the set of G-orbits of the variety N. It turns out that the variety N gives a variant of the Springer correspondence for Weyl groups of type C, but shares a similar flavor with that of type A case. (I.e. there appears...

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 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.

Abstract We prove some qualitative results about the p -adic Jacquet–Langlands correspondence defined by Scholze, in $\operatorname {\mathrm {GL}}_2(\mathbb{Q}_p )$ residually reducible case, using a vanishing theorem proved Judith Ludwig. In particular, we show that cases under consideration, global can also deal with automorphic forms principal series representations at nontrivial way, unlike...

We show that the p-adic Galois representations attached to Hilbert modular forms of motivic weight are potentially semistable at all places above p and are compatible with the local Langlands correspondence at these places, proving this for those forms not covered by the previous works of T. Saito and of D. Blasius and J. Rogawski. 2000 Mathematics Subject Classification: 11F80, 11F41

Certain non-tempered liftings from PGL(2) × PGL(2) to PGSp(4) are constructed using the theory of (local and global) theta lifts. The resulting representations on PGSp(4) are the Saito–Kurokawa representations. The lifting is shown to be functorial under certain reasonable assumptions on the local Langlands correspondence for PGSp(4).