Related papers: $B_{\mathrm{Sen}}$ via distributions on weight spa…

We show that the Fr\'{e}chet space $\mathord{\mathcal{C}^{\infty}}(P)$ of smooth functions on the total space of a surjective submersion $\pi:P\to M$ is a reflexive $\mathord{\mathcal{C}^{\infty}_{c}}(M)$-module.

We construct the fine moduli space of log abelian varieties with PEL structure, which gives a toroidal compactification of the moduli space of abelian varieties with PEL structure.

We consider the system of $N$ ($\ge2$) hard disks of masses $m_1,...,m_N$ and radius $r$ in the flat unit torus $\Bbb T^2$. We prove the ergodicity (actually, the B-mixing property) of such systems for almost every selection…

Twisted commutative algebras (tca's) have played an important role in the nascent field of representation stability. Let A_d be the complex tca freely generated by d indeterminates of degree 1. In a previous paper, we determined the…

By means of appropriate sparse bounds, we deduce compactness on weighted $L^p(w)$ spaces, $1<p<\infty$, for all Calder\'on-Zygmund operators having compact extensions on $L^2(\mathbb{R}^n)$. Similar methods lead to new results on…

The weights for a finite group G with respect to a prime number p where introduced by Jon Alperin, in order to formulate his celebrated conjecture affirming that that the number of G-conjugacy classes of weights of G coincides with the…

We describe the cohomology ring of the moduli space of a flexible polygon in geometrically meaningful terms. We propose two presentations, both are computation friendly: there are simple rules for cup product.

We consider a bounded domain $\Omega \subseteq \mathbb C^d$ which is a $G$-space for a finite complex reflection group $G$. For each one-dimensional representation of the group $G,$ the relative invariant subspace of the weighted Bergman…

Silting modules are abundant. Indeed, they parametrise the definable torsion classes over a noetherian ring, and the hereditary torsion pairs of finite type over a commutative ring. Also the universal localisations of a hereditary ring, or…

The set of periodic distributions, with usual addition and convolution, forms a ring, which is isomorphic, via taking a Fourier series expansion, to the ring ${\mathcal{S}}'({\mathbb{Z}}^d)$ of sequences of at most polynomial growth with…

We study twisted D-modules on the weighted projective stacks. We determine for which values of the twist and the weight the global section functor is an equivalence, thus, proving a version of Beilinson-Bernstein Localisation Theorem.

Let p be a prime. A p-adic functional on a torsion-free abelian group G is a group homomorphism from G to the p-adic integers. The group of all such p-adic functionals is viewed as a p-adic dual group of G, and is studied from the point of…

We develop the $p$-adic representation theory of $p$-adic Lie groups on solid vector spaces over a complete non-archimedean extension of $\mathbb{Q}_p$. More precisely, we define and study categories of solid, solid locally analytic and…

We give proofs of de Rham comparison isomorphisms for rigid-analytic varieties, with coefficients and in families. This relies on the theory of perfectoid spaces. Another new ingredient is the pro-etale site, which makes all constructions…

The classical theory of elliptic curves with complex multiplication is a fundamental tool for studying the arithmetic of abelian extensions of imaginary quadratic fields. While no direct analogue is available for real quadratic fields, a…

We obtain sampling and interpolation theorems in radial weighted spaces of analytic functions for weights of arbitrary (more rapid than polynomial) growth. We give an application to invariant subspaces of arbitrary index in large weighted…

Let $G$ be a compact connected Lie group and $K$ a closed connected subgroup. Assume that the order of any torsion element in the integral cohomology of $G$ and $K$ is invertible in a given principal ideal domain $k$. It is known that in…

For a commutative noetherian ring A, we compare the support of a complex of A-modules with the support of its cohomology. This leads to a classification of all full subcategories of A-modules which are thick (that is, closed under taking…

The symmetrized bidisc has been a rich field of holomorphic function theory and operator theory. A certain well-known reproducing kernel Hilbert space of holomorphic functions on the symmetrized bidisc resembles the Hardy space of the unit…

We answer a question of Alex Koldobsky on isometric embeddings of finite dimensional normed spaces.