A. Polishchuk

collaborators

3 papers

math.AG2026

$L^{2}$ -property for algebraic stacks over local non-archimedean fields

David Kazhdan, Alexander Polishchuk

We introduce an $L^{2}$ -norm on the space of Schwartz half-densities over algebraic stacks over local non-archimedean fields. We show that these $L^{2}$ -norms are finite for the stacks…

math.AG2025

Analog of theta-lifting for a curve over dual numbers over a finite field

David Kazhdan, Alexander Polishchuk

We continue the study of automorphic functions associated with a curve $C$ over the ring $k [I^µ] / (I^µ^{2})$ , where $k$ is a finite field, begun in arXiv:2303.16259. Namely, we study an…

math.AG2025

Schwartz $I^º$ -densities on the moduli stack of rank $2$ bundles near stable bundles

David Kazhdan, Alexander Polishchuk

Let $C$ be a curve over a non-archimedean local field of characteristic zero. We formulate algebro-geometric statements that imply boundedness of functions on the moduli space of s…

L2-property for algebraic stacks over local non-archimedean fields

Analog of theta-lifting for a curve over dual numbers over a finite field

Schwartz I^º-densities on the moduli stack of rank 2 bundles near stable bundles

$L^{2}$ -property for algebraic stacks over local non-archimedean fields

Schwartz $I^º$ -densities on the moduli stack of rank $2$ bundles near stable bundles