A. Polishchuk

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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…

math.AG2024

Schwartz $I^º$ -densities for the moduli stack of rank $2$ bundles on a curve over a local field

Alexander Braverman, David Kazhdan, Alexander Polishchuk

Let $Bun$ be the moduli stack of rank $2$ bundles with fixed determinant on a smooth proper curve $C$ over a local field $F$ . We show how to associate with a Schwartz $I^º$ -den…

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…

math.AG2024

Algebra of global sections of $I ¨ $ -bundles on $M ˉ_{0, n}$

Alexander Polishchuk, Eric Rains

We consider the $Z^{n}$ -graded algebra of global sections of line bundles generated by the standard line bundles $L_{1}, \dots, L_{n}$ on $M ˉ_{0, n}$ . We find a simple prese…

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

Schwartz I^º-densities for the moduli stack of rank 2 bundles on a curve over a local field

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

Algebra of global sections of I¨-bundles on Mˉ0,n​

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

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

Schwartz $I^º$ -densities for the moduli stack of rank $2$ bundles on a curve over a local field

Algebra of global sections of $I ¨ $ -bundles on $M ˉ_{0, n}$