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On the Categorical Approach to the Frobenius Trace


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


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics, Representation Theory, Category Theory, Algebraic Geometry
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Awards:Apostol Award for Excellence in Teaching in Mathematics, 2021. Scott Russell Johnson Prize for Excellence in Graduate Studies, 2020.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Zhu, Xinwen
Thesis Committee:
  • Flach, Matthias (chair)
  • Mantovan, Elena
  • Szumowicz, Anna
  • Zhu, Xinwen
Defense Date:19 May 2023
Record Number:CaltechTHESIS:05052023-230556627
Persistent URL:
Hemo, Tamir0000-0002-0239-6139
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15154
Deposited By: Tamir Hemo
Deposited On:05 Jun 2023 18:02
Last Modified:16 Jun 2023 18:10

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