Multivariable (φ,Γ)-modules and smooth o-torsion representations View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-04

AUTHORS

Gergely Zábrádi

ABSTRACT

Let G be a Qp-split reductive group with connected centre and Borel subgroup B=TN. We construct a right exact functor DΔ∨ from the category of smooth modulo pn representations of B to the category of projective limits of finitely generated étale (φ,Γ)-modules over a multivariable (indexed by the set of simple roots) commutative Laurent series ring. These correspond to representations of a direct power of Gal(Qp¯/Qp) via an equivalence of categories. Parabolic induction from a subgroup P=LPNP gives rise to a basechange from a Laurent series ring in those variables with corresponding simple roots contained in the Levi component LP. DΔ∨ is exact and yields finitely generated objects on the category SPA of finite length representations with subquotients of principal series as Jordan–Hölder factors. Lifting the functor DΔ∨ to all (noncommuting) variables indexed by the positive roots allows us to construct a G-equivariant sheaf Yπ,Δ on G / B and a G-equivariant continuous map from the Pontryagin dual π∨ of a smooth representation π of G to the global sections Yπ,Δ(G/B). We deduce that DΔ∨ is fully faithful on the full subcategory of SPA with Jordan–Hölder factors isomorphic to irreducible principal series. More... »

PAGES

935-995

References to SciGraph publications

Journal

TITLE

Selecta Mathematica

ISSUE

2

VOLUME

24

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00029-016-0259-5

DOI

http://dx.doi.org/10.1007/s00029-016-0259-5

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1028816617


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