Resumen de Character sheaves on unipotent groups in positive characteristic: foundations
Mitya Boyarchenko, Vladimir Drinfeld
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.
