Character sheaves on unipotent groups in positive characteristic: foundations

• Mitya Boyarchenko ^[1] ; Vladimir Drinfeld ^[2]
  1. [1] University of Michigan–Ann Arbor

     University of Michigan–Ann Arbor

     City of Ann Arbor, Estados Unidos

     
  2. [2] University of Chicago

     University of Chicago

     City of Chicago, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 20, Nº. 1, 2014, págs. 125-235
• Idioma: inglés
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• Resumen

  • In this article we formulate and prove the main theorems of the theory of character sheaves on unipotent groups over an algebraically closed field of characteristic p>0. In particular, we show that every admissible pair for such a group G gives rise to an L-packet of character sheaves on G and that conversely, every L-packet of character sheaves on G arises from a (nonunique) admissible pair. In the Appendices we discuss two abstract category theory patterns related to the study of character sheaves. The first Appendix sketches a theory of duality for monoidal categories, which generalizes the notion of a rigid monoidal category and is close in spirit to the Grothendieck–Verdier duality theory. In the second one we use a topological field theory approach to define the canonical braided monoidal structure and twist on the equivariant derived category of constructible sheaves on an algebraic group; moreover, we show that this category carries an action of the surface operad. The third Appendix proves that the “naive” definition of the equivariant ℓ-adic derived category with respect to a unipotent algebraic group is equivalent to the “correct” one.