Mirror symmetry and the K theory of a p-adic group
Author(s)
Vaintrob, Dmitry
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Massachusetts Institute of Technology. Department of Mathematics.
Advisor
Roman Bezrukavnikov.
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Let G be a split, semisimple p-adic group. We construct a derived localization functor Loc : ... from the compactified category of [BK2] associated to G to the category of equivariant sheaves on the Bruhat-Tits building whose stalks have finite-multiplicity isotypic components as representations of the stabilizer. Our construction is motivated by the "coherent-constructible correspondence" functor in toric mirror symmetry and a construction of [CCC]. We show that Loc has a number of useful properties, including the fact that the sections ... compactifying the finitely-generated representation V. We also construct a depth </= e "truncated" analogue Loc(e) which has finite-dimensional stalks, and satisfies the property RIP ... V of depth </= e. We deduce that every finitely-generated representation of G has a bounded resolution by representations induced from finite-dimensional representations of compact open subgroups, and use this to write down a set of generators for the K-theory of G in terms of K-theory of its parahoric subgroups.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016. Cataloged from PDF version of thesis. Includes bibliographical references (pages 59-61).
Date issued
2016Department
Massachusetts Institute of Technology. Department of MathematicsPublisher
Massachusetts Institute of Technology
Keywords
Mathematics.