Geometrization of Trace Formulas
arXiv:1004.5323
Abstract
Following our joint work arXiv:1003.4578 with Robert Langlands, we make the first steps toward developing geometric methods for analyzing trace formulas in the case of the function field of a curve defined over a finite field. We also suggest a conjectural framework of geometric trace formulas for curves defined over the complex field, which exploits the categorical version of the geometric Langlands correspondence.
62 pages; conjectural Atiyah-Bott-Lefschetz fixed point formula for stacks is elucidated. To appear in Bulletin of Mathematical Sciences, Springer-Verlag