Higher arithmetic theta series
Tony Feng (MIT)
Abstract: Arithmetic theta series are incarnations of theta functions in arithmetic algebraic geometry. The first examples were constructed by Kudla as generating series of special cycles on Shimura varieties. Their conjectural key features are (1) modularity of the generating series, and (2) the arithmetic Siegel-Weil formula, relating their enumerative geometry to the first derivative of Eisenstein series at special values. In joint work with Zhiwei Yun and Wei Zhang, we construct "higher" arithmetic theta series on moduli spaces of shtukas, which we conjecture to also enjoy (1) modularity and (2) a higher arithmetic Siegel-Weil formula relating their enumerative geometry to all derivatives of Eisenstein series at special values. We prove several results towards these conjectures, drawing upon ideas from Ngo's proof of the Fundamental Lemma in addition to new ingredients from Springer theory and derived algebraic geometry.
number theory
Audience: researchers in the topic
University of Arizona Algebra and Number Theory Seminar
Organizers: | Aparna Upadhyay*, Pan Yan* |
*contact for this listing |