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9781470453763 Academic Inspection Copy

Coefficient Systems on the Bruhat-Tits Building and Pro-$p$ Iwahori-Hecke Modules

  • ISBN-13: 9781470453763
  • Publisher: AMERICAN MATHEMATICAL SOCIETY
    Imprint: AMERICAN MATHEMATICAL SOCIETY
  • By Jan Kohlhaase
  • Price: AUD $219.00
  • Stock: 0 in stock
  • Availability: This book is temporarily out of stock, order will be despatched as soon as fresh stock is received.
  • Local release date: 28/02/2023
  • Format: Paperback (254.00mm X 178.00mm) 69 pages Weight: 363g
  • Categories: Algebra [PBF]Algebraic geometry [PBMW]
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Let G be the group of rational points of a split connected reductive group over a nonarchimedean local field of residue characteristic p.LetI be a pro-p Iwahori subgroup of G and let R be a commutative quasi-Frobenius ring. If H = R[I\G/I] denotes the pro-p Iwahori- Hecke algebra of G over R we clarify the relation between the category of H-modules and the category of G-equivariant coefficient systems on the semisimple Bruhat-Tits building of G.IfR is a field of characteristic zero this yields alternative proofs of the exactness of the Schneider-Stuhler resolution and of the Zelevinski conjecture for smooth G-representations generated by their I-invariants. In general, it gives a description of the derived category of H-modules in terms of smooth G-representations and yields a functor to generalized (?, ?)-modules extending the constructions of Colmez, Schneider and Vign?eras.
Jan Kohlhaase, Universitat Duisburg-Essen, Germany.
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