Polishchuk 9700458 This research is concerned with generalizing the approach of character sheaves from the case of groups over finite fields to groups over p-adic fields. The work involves two parts. The first part is to devise a notion of sheaves on ind-schemes mimicking that of locally-constant functions on p-adic varieties. The second part is to generalize the Lefschetz-Verdier trace formula and its application to the construction of the discrete series representation of a reductive group over a finite field based on the gluing of perverse sheaves. This is research in the field of algebraic geometry. Algebraic geometry is one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in physics, theoretical computer science, and robotics.
