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

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

(Autor)

Buch | Softcover
69 Seiten
2022
American Mathematical Society (Verlag)
978-1-4704-5376-3 (ISBN)
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In general, this volume 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 Vigneras.
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.

Erscheinungsdatum
Reihe/Serie Memoirs of the American Mathematical Society
Verlagsort Providence
Sprache englisch
Maße 178 x 254 mm
Gewicht 363 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 1-4704-5376-2 / 1470453762
ISBN-13 978-1-4704-5376-3 / 9781470453763
Zustand Neuware
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