Do you want to publish a course? Click here

The L-group of a covering group

222   0   0.0 ( 0 )
 Added by Martin Weissman
 Publication date 2015
  fields
and research's language is English




Ask ChatGPT about the research

We incorporate nonlinear covers of quasisplit reductive groups into the Langlands program, defining an L-group associated to such a cover. This L-group is an extension of the absolute Galois group of a local or global field $F$ by a complex reductive group. The L-group depends on an extension of a quasisplit reductive $F$-group by $mathbf{K}_2$, a positive integer $n$ (the degree of the cover), an injective character $epsilon colon mu_n rightarrow {mathbb C}^times$, and a separable closure of $F$. Our L-group is consistent with previous work on covering groups, and its construction is contravariantly functorial for certain well-aligned homomorphisms. An appendix surveys torsors and gerbes on the etale site, as they are used in a crucial step in the construction.



rate research

Read More

180 - Martin H. Weissman 2015
We incorporate covers of quasisplit reductive groups into the Langlands program, defining an L-group associated to such a cover. We work with all covers that arise from extensions of quasisplit reductive groups by $mathbf{K}_2$ -- the class studied by Brylinski and Deligne. We use this L-group to parameterize genuine irreducible representations in many contexts, including covers of split tori, unramified representations, and discrete series for double covers of semisimple groups over $mathbb R$. An appendix surveys torsors and gerbes on the etale site, as they are used in the construction of the L-group.
318 - Gaetan Chenevier 2013
Let G be a profinite group which is topologically finitely generated, p a prime number and d an integer. We show that the functor from rigid analytic spaces over Q_p to sets, which associates to a rigid space Y the set of continuous d-dimensional pseudocharacters G -> O(Y), is representable by a quasi-Stein rigid analytic space X, and we study its general properties. Our main tool is a theory of determinants extending the one of pseudocharacters but which works over an arbitrary base ring; an independent aim of this paper is to expose the main facts of this theory. The moduli space X is constructed as the generic fiber of the moduli formal scheme of continuous formal determinants on G of dimension d. As an application to number theory, this provides a framework to study the generic fibers of pseudodeformation rings (e.g. of Galois representations), especially in the residually reducible case, and including when p <= d.
119 - Martin H. Weissman 2016
In one article, the author has defined an L-group associated to a cover of a quasisplit reductive group over a local or global field. In another article, Wee Teck Gan and Fan Gao define (following an unpublished letter of the author) an L-group associated to a cover of a pinned split reductive group over a local or global field. In this short note, we give an isomorphism between these L-groups. In this way, the results and conjectures discussed by Gan and Gao are compatible with those of the author. Both support the same Langlands-type conjectures for covering groups.
Let k be any field. We consider the Hopf-Schur group of k, defined as the subgroup of the Brauer group of k consisting of classes that may be represented by homomorphic images of Hopf algebras over k. We show here that twisted group algebras and abelian extensions of k are quotients of cocommutative and commutative Hopf algebras over k, respectively. As a consequence we prove that any tensor product of cyclic algebras over k is a quotient of a Hopf algebra over k, revealing so that the Hopf-Schur group can be much larger than the Schur group of k.
176 - Mahdi Asgari , Ralf Schmidt 2007
We explicitly compute the adjoint L-function of those L-packets of representations of the group GSp(4) over a p-adic field of characteristic zero that contain non-supercuspidal representations. As an application we verify a conjecture of Gross-Prasad and Rallis in this case. The conjecture states that the adjoint L-function has a pole at s=1 if and only if the L-packet contains a generic representation.
comments
Fetching comments Fetching comments
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا