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Geometric Weil representation in characteristic two

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  13 December 2011

Alain Genestier  and
Sergey Lysenko
Alain Genestier
Affiliation:
Institut Elie Cartan, Université Henri Poincaré Nancy 1, BP 239, F-54506 Vandoeuvre-lès-Nancy Cedex, France ([email protected]; [email protected])
Sergey Lysenko
Affiliation:
Institut Elie Cartan, Université Henri Poincaré Nancy 1, BP 239, F-54506 Vandoeuvre-lès-Nancy Cedex, France ([email protected]; [email protected])
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Abstract

Let k be an algebraically closed field of characteristic two. Let R be the ring of Witt vectors of length two over k. We construct a group stack Ĝ over k, the metaplectic extension of the Greenberg realization of . We also construct a geometric analogue of the Weil representation of Ĝ, this is a triangulated category on which Ĝ acts by functors. This triangulated category and the action are geometric in a suitable sense.

Keywords

Weil representationcharacteristic twometaplectic extension

MSC classification

Secondary: 11R39: Langlands-Weil conjectures, nonabelian class field theory
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 11 , Issue 2 , April 2012 , pp. 221 - 271
Copyright
Copyright © Cambridge University Press 2012

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