Related papers: Affinoids in the Lubin-Tate perfectoid space and s…
We construct a family of affinoids in the Lubin-Tate perfectoid space and their formal models such that the middle cohomology of their reductions realizes the local Langlands correspondence and the local Jacquet-Langlands correspondence for…
Following Weinstein, Boyarchenko-Weinstein and Imai-Tsushima, we construct a family of affinoids in the Lubin-Tate perfectoid space and formal models such that the cohomology of the reduction of each formal model realizes the local…
We propose a geometric strategy of giving explicit description of the Langlands parameter of an irreducible supercuspidal representation of GL(n) over a non-archimedean local field. The key is to compare the cohomology of an affinoid in the…
In this paper, we define a family of affinoids in the tubular neighborhoods of CM points in the Lubin-Tate curve with suitable level structures, and compute the reductions of them in the equal characteristic case. By using etale cohomology…
For two distinct primes p and l, we investigate the Z_l-cohomology of the Lubin-Tate towers of a p-adic field. We prove that it realizes some version of Langlands and Jacquet-Langlands correspondences for flat families of irreducible…
We analyze the geometry of the tower of Lubin-Tate deformation spaces, which parametrize deformations of a one-dimensional formal module of height h together with level structure. According to the conjecture of Deligne-Carayol, these spaces…
In this article, we study the De Rham cohomology of the first cover in the Lubin-Tate tower. In particular, we get a purely local proof that the supercuspidal part realizes the local Jacquet-Langlands correspondence for ${\rm GL}_n$ by…
The cohomology of the Lubin-Tate tower is known to realize the local Langlands correspondence for GL(n) over a nonarchimedean local field. In this article we make progress towards a purely local proof of this fact. To wit, we find a family…
Harris and Taylor proved that the supercuspidal part of the cohomology of the Lubin-Tate tower realizes both the local Langlands and Jacquet-Langlands correspondences, as conjectured by Carayol. Recently, Boyer computed the remaining part…
We conjecture that quantum Gaudin models in affine types admit families of local higher Hamiltonians, labelled by the (countably infinite set of) exponents, whose eigenvalues are given by functions on a space of meromorphic opers associated…
We construct integral models and special affinoids of suitable tubular neighborhoods of local Shimura varieties at depth-zero. We show that the reductions of the special affinoids over suitable tamely ramified extensions are realized as…
The conjecture stated by Carayol in [{\em Non-abelian Lubin-Tate theory.} Automorphic forms, Shimura varieties and $L$-functions, vol II: 15--39, Academic Press,1990] predicted that the {\em supercuspidal part} of the l-adic cohomology of…
Let $O$ be the ring of power series in one variable over a finite field, with $K$ its fraction field. We introduce the notion of a "formal $K$-vector space"; this is a certain kind of $K$-vector space object in the category of formal…
We prove that the p-adic local Langlands correspondence for GL_2(Q_p) appears in the etale cohomology of the Lubin-Tate tower at infinity. We use global methods using recent results of Emerton on the local-global compatibility and hence our…
In this paper, we compute irreducible components which appear in the stable reduction of the Lubin-Tate curve of level two, in the mixed characteristic case. We also compute the action of the central division algebra of invariant 1/2, the…
We construct the local Galois representations over the complex field whose Swan conductors are one by using etale cohomology of Artin-Schreier sheaves on affine lines over finite fields. Then, we study the Galois representations, and give…
Let $p$ be an odd prime. Let $F$ be a non-archimedean local field of residue characteristic $p$, and let $\mathbb{F}_q$ be its residue field. Let $\mathcal{H}^{(1)}_{\mathbb{F}_q}$ be the pro-$p$-Iwahori-Hecke algebra of the $p$-adic group…
We will give an explicit construction of irreducible suparcuspidal representations of the special linear group over a non-archimedean local field and will speculate its Langlands parameter by means of verifying the Hiraga-Ichino-Ikeda…
We study the geometry and cohomology of the (generic fibres) of formal deformation schemes of one-dimensional formal modules of finite height. By the work of Boyer (in mixed characterististic) and Harris and Taylor, the l-adic etale…
Gaudin hamiltonians form families of r-dimensional abelian Lie subalgebras of the holonomy Lie algebra of the arrangement of reflection hyperplanes of a Coxeter group of rank r. We consider the set of principal Gaudin subalgebras, which is…