2024 Dmodules and automorphic induction

Dmodules and automorphic induction

Author: xwyg

August undefined, 2024

WebAug 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 ... WebNov 25, 2003 · An example of non-normal quintic automorphic induction and modularity of symmetric powers of cusp forms of icosahedral type Henry H. Kim 1 Inventiones mathematicae volume 156 , pages 495–502 ( 2004 ) Cite this article

NOTES ON AUTOMORPHIC FORMS OF GL(2)

WebQuintic 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 representation of the Galois group ρ: GQ−→ GL 2(C).The converse is a special case of a strong Artin conjecture, namely, given an odd irreducible representation 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 ... microsoft office for my laptop

(PDF) Quasi-Tempered Automorphic D-modules - ResearchGate

Webforms via base change and automorphic induction. In a few cases these constructions have already been made, as a consequence of a lot of work([1], for example). The local and global compatibility of ... Kisin’s work on the Dieudonn e module associated to a p-adic modular form, and will no doubt have other applications. 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, … WebDrinfeld 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 … how to create a file using matlab

Base-Change and Automorphic-Induction for $GL_1$

WebQuintic 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 … 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 … microsoft office for my pcWebMay 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 ... microsoft office for nus students

"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 ... " - Dmodules and automorphic induction

Dmodules and automorphic induction

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

WebGLp2q-Modules and Applications to Automorphic Representations Gal Dor Tel-Aviv University July 01, 2024 1/22. Introduction p-adic representations GJ vs. JL Monoidal structure Apology Global theory Introduction L-functions are important objects. When the L-functions are equal: get deep connections across WebLet K be a quadratic imaginary field. Let Π (resp. Π1) be a regular algebraic cuspidal representation of GLnpAKq (resp. GLn ́1pAKq) which is moreover cohomological and …

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http://faculty.bicmr.pku.edu.cn/~lxiao/2024spring/Notes9-Lu.pdf Webfor the automorphic induction exists for generic cuspidal automorphic representations. By using this automorphic induction, we give a con-jectural criterion on the existence of poles of L(s;ˇ;^3 ˜) for discrete automorphic representations in the tempered spectrum. Contents 1. Introduction2 2. Integral representation5 2.1. Global zeta ...

WebDual module. In mathematics, the dual module of a left (respectively right) module M over a ring R is the set of module homomorphisms from M to R with the pointwise right …

WebIt is conjectured that an automorphic representation of GL n associated to K induces an automorphic representation of GL r n associated to F. The book by Arthur and Clozel … Web6. 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.

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 …

WebDear all, I try to understand the base-change and automorphic-induction in the theory of automorphic forms, for the simplest case: G L 1. Both are implied by Langlands … how to create a file typeWebDe 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 ... microsoft office for one computerWebOct 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 – … microsoft office for new macbook proWebAug 19, 2024 · The existence of (non-zero) such residues is determined by the analytic behavior of the Eisenstein series at \nu =\nu _0, which is closely related to the analytic behavior of the automorphic L -functions in its constant term, according to the Langlands–Shahidi method [ 4, 10, 19, 20 ]. microsoft office for nonprofitWebMay 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 ... how to create a file using nanoWebalgebra 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 ... microsoft office for non profit organizationWebMay 1, 2010 · For F=R or C, isomorphism classes of irreducible (g,K)-modules for GL(n,F) are parametrized by n-dimensional representations of the Weil group WF of F. ... how to create a filereader in java