Abstract
In this paper we prove a general vanishing result for Kohlhaase’s higher smooth duality functors . If is any unramified connected reductive -adic group, is a hyperspecial subgroup, and is a Serre weight, we show that for , where is a Borel subgroup and the dimension is over . This is due to Kohlhaase for , in which case it has applications to the calculation of 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
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
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