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2019 A vanishing result for higher smooth duals
Claus Sorensen
Algebra Number Theory 13(7): 1735-1763 (2019). DOI: 10.2140/ant.2019.13.1735

Abstract

In this paper we prove a general vanishing result for Kohlhaase’s higher smooth duality functors Si. If G is any unramified connected reductive p-adic group, K is a hyperspecial subgroup, and V is a Serre weight, we show that Si(indKGV)=0 for i> dim(GB), where B is a Borel subgroup and the dimension is over p. This is due to Kohlhaase for GL2(p), in which case it has applications to the calculation of Si for supersingular representations. Our proof avoids explicit matrix computations by making use of Lazard theory, and we deduce our result from an analogous statement for graded algebras via a spectral sequence argument. The graded case essentially follows from Koszul duality between symmetric and exterior algebras.

Citation

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Claus Sorensen. "A vanishing result for higher smooth duals." Algebra Number Theory 13 (7) 1735 - 1763, 2019. https://doi.org/10.2140/ant.2019.13.1735

Information

Received: 1 October 2018; Revised: 27 March 2019; Accepted: 21 May 2019; Published: 2019
First available in Project Euclid: 16 January 2020

zbMATH: 07110520
MathSciNet: MR4009675
Digital Object Identifier: 10.2140/ant.2019.13.1735

Subjects:
Primary: 20C08
Secondary: 22E50

Keywords: higher smooth duality , Lazard theory , mod p representations

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.13 • No. 7 • 2019
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