A. Polishchuk

activity

20242026

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 $k [ε] / (ε^{2})$ , where $k$ is a finite field, begun in arXiv:2303.16259. Namely, we study an e…

math.AG2024

Superperiods and superstring measure near the boundary of the moduli space of supercurves

Giovanni Felder, David Kazhdan, Alexander Polishchuk

We study the behavior of the superperiod map near the boundary of the moduli space of stable supercurves and prove that it is similar to the behavior of periods of classical curves…

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

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

Superperiods and superstring measure near the boundary of the moduli space of supercurves

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