On the Categorical Approach to the Frobenius Trace

Author: Hemo, Tamir

Year: 2023

Degree: Dissertation (Ph.D.)

Advisor: Zhu, Xinwen

Committee Members: Flach, Matthias; Mantovan, Elena; Szumowicz, Anna; Zhu, Xinwen

Option: Mathematics

DOI: 10.7907/8d25-ky12

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.

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