Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 20 of 32 for “"Langlands"”.
-
Geometric Langlands in prime characteristic
… algebraic group over k and let GV be its Langlands dual group over k. Denote by BunG the moduli stack of G-bundles on C and LocSysGv the moduli stack of Gv-local systems on C. Let DBunG be the sheaf of crystalline differential operator algebra on BunG. In this thesis I construct an …
-
Positive traces and analytic Langlands correspondence
… traces. The second direction is analytic Langlands correspondence, which is the following. Let X be a smooth irreducible projective curve over C, G be a complex reductive group. On one side of this conjectural correspondence there are G superscript v -opers on X satisfying a certain …
-
The p-adic local langlands conjecture
… simply connected groups are pure. A p-adic Local Langlands correspondence would assign an L-packet, consisting of finitely many admissible representations of a p-adic group, to each Langlands parameter. To identify particular representations, data extending a Langlands parameter is needed to make …
-
Kategorielle Langlands-Korrespondenz für die verallgemeinerten Lorentz-Gruppen
Im Rahmen der lokalen Langlands-Philosophie für die reellen Zahlen konstruieren Adams, Barbasch und Vogan eine Bijektion zwischen den einfachen Harish-Chandra-Moduln zu einer reellen reduktiven Gruppe G und dem Raum <br>der "vollständigen geometrischen Parameter" - einer Menge von äquivarianten …
-
Tamely ramified geometric Langlands correspondence in positive characteristic
… prove a version of the tamely ramified geometric Langlands correspondence in positive characteristic for GLn(k), where k is an algebraically closed field of characteristic p > n. Let X be a smooth projective curve over k with marked points, and fix a parabolic subgroup of GLn(k) at each marked …
-
Some results related to the quantum geometric Langlands program
… G and the category of representations of its Langlands dual group. The category of spherical perverse sheaves sits naturally in an equivariant derived category, and this larger category was described in terms of the dual group by Bezrukavnikov-Finkelberg. Recently, Finkelberg-Lysenko proved a …
-
Langlands Duality in the Generic Fibres of Classical Hitchin Fibrations
… torsors of abelian varieties, and we demonstrate Langlands duality in the Hitchin bration by proving the generic bres corresponding to Langland's dual groups are indeed dual abelian varieties. The thesis consists of two parts. In Part I, we review the necessary background of complex algebraic …
-
Quantum geometric Langlands correspondence in positive characteristic: the GLN case
Let C be a smooth connected projective curve of genus > 1 over an algebraically closed field k of characteristic p > 0, and c [epsilon] k \ Fp. Let BunN be the stack of rank N vector bundles on C and Ldet the line bundle on BunN given by determinant of derived global sections. In this thesis, we …
-
Nearby cycles and the cohomology of shtukas
V. Lafforgue constructed Langlands parameters from automorphic forms for any reductive group over a function field using excursion operators. Our aim is to give a general approach for proving certain local-global compatibilities satisfied by these Langlands parameters. The main consequence for the …
-
Approximate converse theorem
… of PGL(n, A), n ≥ 1. For a given set of Langlands parameters for some places of Q, we can compute ε > 0 such that there exists a genuine globally unramified cuspidal representation, whose Langlands parameters are within ε of the given ones for finitely many places.
-
Derived Geometric Satake Equivalence, Springer Correspondence, and Small Representations
… when restricting to small representations of the Langlands dual group (see a paper by Achar and Henderson and one by Achar, Henderson, and Riche). This dissertation relates the derived geometric Satake equivalence of Bezrukavnikov and Finkelberg and the derived Springer correspondence of Rider …
-
Equivariant quantum cohomology and the geometric Satake equivalence
… a fundamental space in the geometric Langlands program. More precisely, we identify the equivariant quantum connection of certain symplectic resolutions of slices in the affine Grassmannian of a semisimple group G with a trigonometric Knizhnik-Zamolodchikov (KZ)-type connection of the …
-
Character Theory and Artin L-functions
… Lastly, we study the conjectures of Artin and Langlands via group theory and extend the previous work of Arthur and Clozel. For instance, we introduce the notion of near supersolvability and near nilpotency, and show that Artin's conjecture holds if $\Gal(K/k)$ is nearly supersolvable. As a …
-
Analytic Continuation and Functional Equations of Cuspidal Eisenstein Series for Maximal Cuspidal Subgroups
… suggests an alternative development to part of Langlands' theory of Eisenstein series. It also opens up the possibility of more precise knowledge about the poles of Eisenstein series.
-
Higher Dimensional Adeles, Mean-Periodicity and Zeta Functions of Arithmetic Surfaces
… of the two is a widely believed aspect of the Langlands program. In somewhat vague language, the two notions are dual to each other. One route to this result is broadly comparable to the Rankin-Selberg method, in which Fesenko’s “boundary function” plays the role of an Eisenstein series. 2. The …
-
p-adic L-functions of automorphic forms
… which interpolates the complex (Jacquet-Langlands) L-function at the central critical point. This is a generalization of a construction by Spieß over totally real fields. It seems well-suited to generalize his proof of the exceptional zero conjecture, which describes the order of …
-
SUPERCUSPIDAL REPRESENTATIONS ARISING FROM STABLE VECTORS
… $\{\pi_{v,\rho}\}$ as well as discrete Langlands parameters $\varphi_{v}$. Both the parameter and representations are of depth $a/m$. We further show that for a fixed vector, $\pi_{v,\rho}$ and $\varphi_{v}$ satisfy both sides of the formal degree conjecture.
-
A Coherent Categorification of the Asymptotic Affine Hecke Algebra
… Springer sheaf" on a moduli stack of Deligne–Langlands parameters whose endomorphism algebra recovers H. In this thesis, we extend these results to Lusztig's asymptotic affine Hecke algebra J. Using work of Bezrukavnikov–Ostrik, we construct an "asymptotic coherent Springer sheaf" on an …
-
Equivariant coherent sheaves, Soergel bimodules, and categorification of affine Hecke algebras
… sheaves on the affine flag manifold (for the Langlands dual group). We prove results relating all three of these categorifications, and use them to deduce nontrivial equivalences of categories. In addition, our main theorem allows us to deduce the existence of a strict braid group action on …
Page 1 of 2