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Deformation theory and finite simple quotients of triangle groups I

Michael Larsen, Alexander Lubotzky, Claude Marion (2014)

Journal of the European Mathematical Society

Let 2 a b c with μ = 1 / a + 1 / b + 1 / c < 1 and let T = T a , b , c = x , y , z : x a = y b = z c = x y z = 1 be the corresponding hyperbolic triangle group. Many papers have been dedicated to the following question: what are the finite (simple) groups which appear as quotients of T ? (Classically, for ( a , b , c ) = ( 2 , 3 , 7 ) and more recently also for general ( a , b , c ) .) These papers have used either explicit constructive methods or probabilistic ones. The goal of this paper is to present a new approach based on the theory of representation varieties (via deformation theory). As a corollary we essentially prove...

Deformations and derived categories

Frauke M. Bleher, Ted Chinburg (2005)

Annales de l'institut Fourier

In this paper we generalize the deformation theory of representations of a profinite group developed by Schlessinger and Mazur to deformations of objects of the derived category of bounded complexes of pseudocompact modules for such a group. We show that such objects have versal deformations under certain natural conditions, and we find a sufficient condition for these versal deformations to be universal. Moreover, we consider applications to deforming Galois cohomology classes and the étale hypercohomology...

Dehn twists on nonorientable surfaces

Michał Stukow (2006)

Fundamenta Mathematicae

Let t a be the Dehn twist about a circle a on an orientable surface. It is well known that for each circle b and an integer n, I ( t a ( b ) , b ) = | n | I ( a , b ) ² , where I(·,·) is the geometric intersection number. We prove a similar formula for circles on nonorientable surfaces. As a corollary we prove some algebraic properties of twists on nonorientable surfaces. We also prove that if ℳ(N) is the mapping class group of a nonorientable surface N, then up to a finite number of exceptions, the centraliser of the subgroup of ℳ(N) generated...

Deligne-Lusztig restriction of a Gelfand-Graev module

Olivier Dudas (2009)

Annales scientifiques de l'École Normale Supérieure

Using Deodhar’s decomposition of a double Schubert cell, we study the regular representations of finite groups of Lie type arising in the cohomology of Deligne-Lusztig varieties associated to tori. We deduce that the Deligne-Lusztig restriction of a Gelfand-Graev module is a shifted Gelfand-Graev module.

Currently displaying 41 – 60 of 220