Related papers: A geometric proof of Duflo's Theorem

In the context of supersymmetric quantum mechanics we formulate new supersymmetric localization principle, with application to trace formulas for a full thermal partition function. Unlike the standard localization principle, this new…

Foundational material on complex Lie supergroups and their radial operators is presented. In particular, Berezin's recursion formula for describing the radial parts of fundamental operators in general linear and ortho-symplectic cases is…

We prove new, general versions of Bernstein-von Mises theorem for both well-specified and misspecified models when the log-likelihood is concave in the parameter and the prior distribution is log-concave. Unlike classical versions of…

Let (S,L) be a Lie-Rinehart algebra over a commutative ring R. This article proves that, if S is flat as an R-module and has Van den Bergh duality in dimension n, and if L is finitely generated and projective with constant rank d as an…

In this text, we outline a theory of schemes associated with a site, which generalizes a variety of geometries, such as manifolds, schemes, analytic spaces, simplicial complexes, and more. We present an abstract process of gluing model…

Suppose $R$ is a commutative ring with identity and a fixed invertible element $q^{\frac{1}{2}}$ such that $q+q^{-1}$ is invertible. For an oriented surface $\Sigma$, let $\mathcal{S}(\Sigma;R)$ denote the Kauffman bracket skein algebra of…

In this paper, we first establish the localization of the Bergman kernels for unbounded pseudoconvex domains near a D'Angelo finite type boundary point. This result was proved by Engli\v{s} more than twenty years ago for bounded…

Combining the tools of geometric analysis with properties of Jordan angles and angle space distributions, we derive a spherical and a Euclidean Bernstein theorem for minimal submanifolds of arbitrary dimension and codimension, under the…

In this paper, we prove the following version of the famous Bernstein's theorem: Let $X\subset \mathbb R^{n+k}$ be a closed and connected set with Hausdorff dimension $n$. Assume that $X$ satisfies the monotonicity formula at $p\in X$.…

In this paper all rings are commutative. We prove some new results on flat epimorphisms of rings and pointwise localizations. Especially among them, it is proved that a ring $R$ is an absolutely flat (von-Neumann regular) ring if and only…

Given a projective scheme $X$ over a field $k$, an automorphism $\sigma$ of $X$, and a $\sigma$-ample invertible sheaf $L$, one may form the twisted homogeneous coordinate ring $B = B(X, L, \sigma)$, one of the most fundamental…

We consider Lie algebroids over an algebraic space (or topological ringed space) as quasicoherent sheaves of Lie-Rinehart algebras. We express hypercohomology for a locally free Lie algebroid (not necessarily of finite rank) as a derived…

In this paper we prove a generalisation of Schlenk's theorem about the existence of contractible periodic Reeb orbits on stable, displaceable hypersurfaces in symplectically aspherical, geometrically bounded, symplectic manifolds, to a…

In this paper, we study the cohomology of semisimple local systems in the spirit of classical Hodge theory. On the one hand, we establish a generalization of Hodge-Riemann bilinear relations. For a semisimple local system on a smooth…

We show that a formal Deligne--Mumford stack is formal-locally represented by a formal scheme. This is an analogue of Frobenius theorem for smooth foliations in any characteristic and without smoothness hypotheses on the ambient space.

We investigate color Lie rings over finite group algebras and their universal enveloping algebras. We exhibit these universal enveloping algebras as PBW deformations of skew group algebras: Every color Lie ring over a finite group algebra…

We describe the prime and primitive spectra for quantized enveloping algebras at roots of 1 in characteristic zero in terms of the prime spectrum of the underlying enveloping algebra. For primitive ideals we obtain an analogue of Duflo's…

We give a generalization of Gabriel's Theorem on coherent sheaves to the case of coherent twisted sheaves on a smooth variety X over a field k. We show that the category Coh(X,\alpha) determines the scheme structure of X for \alpha in the…

This paper gives an elementary proof of an improved version of the algebraic Local B\'ezout Theorem (given by the authors in JSC 45 (2010) 975--985). Here we remove some ad hoc hypotheses and obtain an optimal algebraic version of the…

We prove that the canonical dimension of a coadmissible representation of a semisimple $p$-adic Lie group in a $p$-adic Banach space is either zero or at least half the dimension of a non-zero coadjoint orbit. To do this we establish…