2024 Dmodules and automorphic induction

Dmodules and automorphic induction

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August undefined, 2024

WebOct 20, 2014 · 27.5.3 Harish-Chandra modules. 27.6 Representations of l-groups: the Hecke algebra. 28 Automorphic forms and the Hecke algebra. 28.1 The case of SL 2 – … WebThe Hodge-Tate period map is an important, new tool for studying the geometry of Shimura varieties, p-adic automorphic forms and torsion classes in the cohomology of Shimura varieties. It is a G (A_f)-equivariant map from a perfectoid Shimura variety into a flag variety with only an action of G (Q_p) and can be thought of as a p-adic analogue ...

Introduction to automorphic representations (DRAFT!)

WebFeb 1, 2024 · This is false in general. Indeed, take the Z module Z / n Z for n ≥ 2. While Z / n Z = n, one can show that there is exactly one group homomorphism (i.e. Z -linear … WebNov 26, 2024 · A D-module (introduced by Mikio Sato) is a sheaf of modules over the sheaf D_X of regular differential operators on a ‘variety’ X (the latter notion depends on … colorful yunnan hawthorn menu

A RAPID INTRODUCTION TO DRINFELD MODULES,

WebMonoidal Structures on GLp2q-Modules and Abstractly Automorphic Representations Gal Dor Tel-Aviv University March 04, 2024 1/24. Introduction p-adic reps GJ vs. JL Monoidal … WebNov 1, 2024 · Using Langlands functoriality and automorphic induction, it gives an automorphic cuspidal representation of GL 2 (A Q). The relation between the automorphic representations of GL 2 (A Q) and the cuspidal cohomology of GL 2 can be described in terms of the sheaf M ˜ μ associated to the highest weight representation M μ of GL (2, … Webalgebra for GLn over CM ﬁelds without needing to assume automorphic induction of characters for the extension K/Q. For this methods of potential automorphy results are used. Contents. 1. Introduction. 1.1. Notation. 2. Preliminaries in commutative algebra. 2.1. Change of coefﬁcients. 2.2. Minimal complexes and the derived category. 2.3 ... colorful youtube banner

Lectures on D-modules. - University of California, …

arXiv:1508.03205v4 [math.NT] 19 Nov 2024

WebCM, i.e., is not the automorphic induction of an algebraic Hecke character from a quadratic CM extension. Let n 1 be an integer. Then the nth symmetric power lifting of ˇexists, in the following sense. There exists an RAESDC automorphic representation ( ; ) of GL n+1(A F) such that for any isomorphism : Q l ˘=C, there is an isomorphism of ... WebMay 1, 2010 · That gives a process of “automorphic induction” which to an irreducible (g,K)- module τ for GL(n,C) associates an irreducible (g,K)-module π = τ C/R for GL(2n,R). In the present paper we show that if τ is unitary and generic then π is determined by τ, up to isomorphism, via a character identity entirely analogous to the character ... colorful yunnan box hillWebAug 6, 2024 · This procedure should conjecturally realize the automorphic induction from T to G. For G = GL_2, we prove that our construction indeed realizes the automorphic induction from at most tamely ... dr shute cardiff

"WebIn mathematics, a D-module is a module over a ring D of differential operators.The major interest of such D-modules is as an approach to the theory of linear partial differential … " - Dmodules and automorphic induction

Dmodules and automorphic induction

WebChapter 2: Automorphic forms and Representations of GL(2;R) In this chapter we study the representation theory of G := GL(2;R)+ or GL(2;R) and its connection with automorphic forms on the upper half plane. The rst manifestation of this inter-action comes from observing that the L2-spaces of automorphic forms of level and that of the Webdrawback. This article contributes to the automorphic induction over local elds by introducing a new construction of type (ii), which works for all tori and all reductive groups (in the equal characteristic case). orF G GL 2 we prove that our construction indeed realizes the ‘-adic automorphic induction for all at most tamely rami ed tori.

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Web11F52 Modular forms associated to Drinfeld modules; 11F55 Other groups and their modular and automorphic forms (several variables) 11F60 Hecke-Petersson operators, ... Lafforgue has proposed a new approach to the principle of functoriality in a test case, namely, the case of automorphic induction from an idele class character of a quadratic ... WebMay 1, 2024 · Automorphic induction of class group characters. Let K / Q be a degree n extension. Let χ be a non-trivial Hecke character of K, and let I K Q χ be the automorphic induction. Since χ is non-trivial, L (s, χ) = L (s, I K Q χ) is entire. However, the automorphy of I K Q χ is proved only in certain cases, namely, it is an automorphic ...

WebDrinfeld Moduli Schemes and Automorphic Forms: The Theory of Elliptic Modules with Applications is based on the author’s original work establishing the correspondence between ell-adic rank r Galois … WebMonoidal Structures on GLp2q-Modules and Abstractly Automorphic Representations Gal Dor Tel-Aviv University July 21, 2024 ... Compact induction of SpM 2pFqqfrom GL 2pFq3;det 1 to GL 2pFq3 gives Y. 11/27. Introduction p-adic reps GJ vs. JL Monoidal …

WebDe nition 1.4. An automorphic representation is a representation of (g;K 1) G(A f) of the form ˇ 1 (0 l ˇ l) which occurs in the cuspidal spectrum decomposition(for some !). Remark. In general, an automorphic representation is an irreducible admissible subrepresen-tation of natural action of (g;K 1) G(A f) on A(G). And automorphic ... WebFeb 1, 2015 · Let K be a quadratic imaginary field. Let Π (resp. Π ′) be a regular algebraic cuspidal representation of GL n (A K) (resp. GL n − 1 (A K)), which is moreover …

WebDRINFELD MODULI SCHEMES AND AUTOMORPHIC FORMS 3 Introduction Let F be a geometric global eld, of characteristic p>0, A its ring of ad eles, G= GL(r) and ˇan …

WebOct 20, 2024 · This is a survey of recent work on values of Rankin-Selberg L-functions of pairs of cohomological automorphic representations that are critical in Deligne’s sense. The base field is assumed to be a CM field. Deligne’s conjecture is stated in the language of motives over \(\mathbb{Q}\), and expresses the critical values, up to rational factors, as … dr shustik west palm beach flWebOct 17, 2024 · quasi-tempered automorphic d-modules 3 consisting of elements ℱ P 𝐷 p Bun 𝐺 q such that if p 𝒫 , 𝜑 q lies in the singular support of ℱ , then 𝜑 factors through z p g q Ď g . dr shusterman philadelphiaWebQuintic automorphic induction 497 respect to a congruence subgroup of SL 2(Z); Deligne-Serre Theorem [D-S] implies that π gives rise to an odd irreducible 2-dimensional … dr shust scranton pa faxWebDrinfeld modules. G. W. Anderson [1] saw correctly how to develop the theory of higher dimensional Drinfeld modules, called t-modules, and at the same time produced a … dr shuster springfield clinicWeb6. Twisted Automorphic Descents 57 6.1. Automorphic descents and certain Arthur packets 57 6.2. Construction of cuspidal automorphic modules 66 6.3. Global Gan-Gross-Prasad conjecture: another direction 69 7. On the Main Conjecture 73 7.1. The main conjecture: general case 73 7.2. The main conjecture: regular orbit case 75 7.3. colorful yunnan hawthornWebApr 1, 2006 · The basics of the theory of Hilbert Q-modules are established. Using this approach to V-semilattices with a duality i.e. Hilbert 2-modules, we describe a nuclear traced ideal and characterize ... dr shuster springfield clinic springfield ilWebALGEBRAIC D-MODULES AND REPRESENTATION THEORY 135 consider the adjoint action of Gon g, the trivial bundle X× g is G-homogeneous and the morphism X×g −→ … dr shutack chesapeake