Links between generalized Montréal-functors

Erdélyi, Márton and Zábrádi, Gergely (2016) Links between generalized Montréal-functors. MATHEMATISCHE ZEITSCHRIFT. pp. 1-49. ISSN 0025-5874 (In Press)

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Abstract

Let o be the ring of integers in a finite extension (Formula presented.) and (Formula presented.) be the (Formula presented.)-points of a (Formula presented.)-split reductive group (Formula presented.) defined over (Formula presented.) with connected centre and split Borel (Formula presented.). We show that Breuil’s (Algebra Number Theory 9(10):2241–2291, 2015) pseudocompact (Formula presented.)-module (Formula presented.) attached to a smooth o-torsion representation (Formula presented.) of (Formula presented.) is isomorphic to the pseudocompact completion of the basechange (Formula presented.) to Fontaine’s ring (via a Whittaker functional (Formula presented.)) of the étale hull (Formula presented.) of (Formula presented.) defined by Schneider and Vigneras (Clay Math Proc 13:525–601, 2011). Moreover, we construct a G-equivariant map from the Pontryagin dual (Formula presented.) to the global sections (Formula presented.) of the G-equivariant sheaf (Formula presented.) on G / B attached to a noncommutative multivariable version (Formula presented.) of Breuil’s (Formula presented.) whenever (Formula presented.) comes as the restriction to B of a smooth, admissible representation of G of finite length. © 2016 Springer-Verlag Berlin Heidelberg

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