On the Categorical Approach to the Frobenius Trace

Citation

Hemo, Tamir (2023) On the Categorical Approach to the Frobenius Trace. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/8d25-ky12. https://resolver.caltech.edu/CaltechTHESIS:05052023-230556627

Abstract

Motivated by the study of the local and global Langlands correspondence from a geometric prespective, we establish two results of a general nature regarding categories of sheaves in algebraic geometry. The first result, motivated by the work of Drinfeld and Lafforgue on the Langlsnds correspondence over function fields, establishes a categorical enhancement of the Künneth formula for categories of Weil sheaves, generalizing a famous result of Drinfeld. In the second part, motivated by the geometric approach to the study of representations of reductive groups over local fields, we develop a method to calculate the categorical trace of monoidal categories arising from convolution pattern in algebraic geometry.

Thesis Files