Mirror symmetry and the K theory of a p-adic group

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2016

Author dc:creator

• Vaintrob, Dmitry

Advisor dc:contributor.advisor

• Roman Bezrukavnikov.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/104578

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/104578