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arXiv · 1201.1874

The Bernstein center of the category of smooth $W(k)[GL_n(F)]$-modules

David Helm
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Abstract

We consider the category of smooth $W(k)[GL_n(F)]$-modules, where F is a p-adic field and k is an algebraically closed field of characteristic l different from p. We describe a factorization of this category into blocks, and show that the center of each block is a reduced, finite type, l-torsion free W(k)-algebra. Moreover, the k-points of the center of each block are in bijection with the possible "supercuspidal supports" of the smooth $k[GL_n(F)]$-modules that lie in the block. Finally, we describe a large, explicit subalgebra of the center of each block and give a description of the action of this subalgebra on the simple objects of the block, in terms of the description of the classical "characteristic zero" Bernstein center.

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David Helm. 2016-05-16. The Bernstein center of the category of smooth $W(k)[GL_n(F)]$-modules. https://arxiv.org/abs/1201.1874

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