David Kazhdan

activity

20232026

collaborators

18 papers

math.RT2026

A proof of Harish-Chandra's integrability theorem for cuspidal representations of $GL_{n} (F_{ℓ} ((t)))$

Avraham Aizenbud, Nir Avni, Dmitry Gourevitch +2

Consider the Chevalley map $p : gl_{n} (F) \to (gl_{n} // GL_{n}) (F),$ where $F = F_{ℓ} ((t))$ . We show that the push forward via $p$ of every smooth…

math.AG2026

Projective connections on super Heisenberg coinvariants. I

Giovanni Felder, David Kazhdan, Alexander Polishchuk

We study derived coinvariants of isotropic subbundles on modules over super Heisenberg algebras and construct and study certain natural transitive Lie algebroids acting on them.

math.RT2026

An analogue of irreducible cuspidal representations for the group $P G L (2)$ over a two-dimensional local field

Alexander Braverman, David Kazhdan

Let $F$ be a local non-archimedian field of odd residue characteristic and let $G = P G L (2)$ . In this paper we study an analog of irreducible cuspidal representations of the group $G(…

math.AG2026

The jet schemes of the nilpotent cone of $gl_{n}$ over $F_{ℓ}$ and analytic properties of the Chevalley map

Avraham Aizenbud, Dmitry Gourevitch, David Kazhdan +1

We prove dimension bounds on the jet schemes of the variety of nilpotent matrices (and of related varieties) in positive characteristic. This result has applications to the analyti…

math.AG2026

Effective local differential topology of algebraic varieties over local fields of positive characteristics

Avraham Aizenbud, Dmitry Gourevitch, David Kazhdan +1

In this paper we provide a framework for quantitative statements on distances and measures when studying algebraic varieties and morphisms of algebraic varieties over local fields.…

math.AG2026

Invertible top form on the Hilbert scheme of a plane in positive characteristic

Avraham Aizenbud, Dmitry Gourevitch, David Kazhdan +1

We prove that the Hilbert scheme of the plane in positive characteristic admits an invertible top differential form. This implies certain integrability properties of the symmetric…

math.RT2026

Orbital integral bounds the character for cuspidal representations of $G L_{n} (F_{ℓ} ((t)))$

Avraham Aizenbud, Dmitry Gourevitch, David Kazhdan +1

We prove that the character of an irreducible cuspidal representation of $G L_{n} (F_{ℓ} ((t)))$ is locally bounded up to a logarithmic factor by the orbital integral of a m…

math.RT2026

On Harish-Chandra's integrability theorem in positive characteristic

Avraham Aizenbud, Dmitry Gourevitch, David Kazhdan +3

The celebrated Harish-Chandra's integrability theorem states that the distributional character of an irreducible smooth representation of a p-adic group $G (F)$ is integrable, that…

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.RT2025

Rationality properties of complex representations of reductive p-adic groups

David Kazhdan, Maarten Solleveld, Yakov Varshavsky

For a reductive group G over a non-archimedean local field, we compare smooth representations over C with smooth representations over Qbar (an algebraic closure of Q). We show that…

math.AG2025

Perversity of coinvariants of affine Springer sheaves

Alexis Bouthier, David Kazhdan, Yakov Varshavsky

Using techniques of [BKV], we construct a perverse t-structure on the infinity-category of l-adic LG-equivariant sheaves on the regular-semisimple bounded locus of the loop group L…

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.AG2025

Endoscopic decomposition of elliptic Fargues-Scholze L-packets

David Kazhdan, Yakov Varshavsky

The main goal of this note is to show that the local L-packet of Fargues-Scholze [FS], corresponding to an elliptic L-parameter, has an endoscopic decomposition. Our argument is st…

math.RT2025

Modular reduction of complex representations of finite reductive groups

Roman Bezrukavnikov, Michael Finkelberg, David Kazhdan +1

The main result describes the Brauer-Nesbitt reduction of unipotent representations of a finite group of Lie type, expressing it as an explicit linear combination of the restrictio…

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

Schwartz $κ$ -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.RT2024

Automorphic functionals for the minimal representations of groups of type $D_{n}$ and $E_{n}$

Nadya Gurevich, David Kazhdan

Let $G$ be a split simply-connected group of type $D$ or $E$ . The minimal automorphic representation $Π$ of $G (A)$ admits a realization on a space of functions $\mathcal S(…

math.NT2023

L-function genera and applications

David Kazhdan, Andrei Okounkov

We introduce equivariant L-genera associated to actions of Galois and related groups on algebraic varieties. We explain the role which these L-genera play in the spectral analysis…

A proof of Harish-Chandra's integrability theorem for cuspidal representations of GLn​(Fℓ​((t)))

Projective connections on super Heisenberg coinvariants. I

An analogue of irreducible cuspidal representations for the group PGL(2) over a two-dimensional local field

The jet schemes of the nilpotent cone of gln​ over Fℓ​ and analytic properties of the Chevalley map

Effective local differential topology of algebraic varieties over local fields of positive characteristics

Invertible top form on the Hilbert scheme of a plane in positive characteristic

Orbital integral bounds the character for cuspidal representations of GLn​(Fℓ​((t)))

On Harish-Chandra's integrability theorem in positive characteristic

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

Rationality properties of complex representations of reductive p-adic groups

Perversity of coinvariants of affine Springer sheaves

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

Endoscopic decomposition of elliptic Fargues-Scholze L-packets

Modular reduction of complex representations of finite reductive groups

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

Schwartz κ-densities on the moduli stack of rank 2 bundles near stable bundles

Automorphic functionals for the minimal representations of groups of type Dn​ and En​

L-function genera and applications

A proof of Harish-Chandra's integrability theorem for cuspidal representations of $GL_{n} (F_{ℓ} ((t)))$

An analogue of irreducible cuspidal representations for the group $P G L (2)$ over a two-dimensional local field

The jet schemes of the nilpotent cone of $gl_{n}$ over $F_{ℓ}$ and analytic properties of the Chevalley map

Orbital integral bounds the character for cuspidal representations of $G L_{n} (F_{ℓ} ((t)))$

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

Schwartz $κ$ -densities on the moduli stack of rank $2$ bundles near stable bundles

Automorphic functionals for the minimal representations of groups of type $D_{n}$ and $E_{n}$