Year: 2023
Type: preprint
Abstract: In this paper, we introduce a new class of $\ell$-adic sheaves, which we call quadratic $\ell$-adic sheaves, on connected unipotent commutative algebraic groups over finite fields. They are sheaf-theoretic enhancements of quadratic forms on finite abelian groups in the spirit of the function-sheaf dictionary. We show that a certain finite Heisenberg group acts on a quadratic sheaf and that the cohomology of the quadratic sheaf gives an irreducible representation of the group. We also compute the Frobenius eigenvalues of the cohomology groups. As a byproduct, we find a large number of examples of affine supersingular varieties.
Source: arXiv (Cornell University)
Author: Takeuchi, Daichi
Institution: RIKEN Center for Advanced Intelligence Project
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4378474122