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math.AG2026
On the excursion algebra
Dennis Gaitsgory, Kevin Lin, Wyatt Reeves
The excursion algebra associated to a scheme X over a finite field and a reductive group G is the algebra of global functions on the stack of arithmetic G-local systems on X. When…
math.AG2026
Applications of (higher) categorical trace II: Deligne-Lusztig theory
D. Gaitsgory, N. Rozenblyum, Y. Varshavsky
We use the formalism of the (2-category) AGCat, developed in [GRV], and the operation of higher categorical trace to (re)derive a number of results in the Deligne-Lusztig theory.
math.AG2025
Representations of loop groups as factorization module categories
Lin Chen, Yuchen Fu, Dennis Gaitsgory +1
We show that the (2-)category of categorical representations of the loop group embeds fully faithfully into the (2-)category of factorization module categories with respect to the…