Related papers: Elliptic Dedekind Domains Revisited

Let $A$ be an affinoid integral domain over a non-Archimedean field $K$, and let $L$ be its field of fractions. We prove that the normalization of $A$ can be reconstructed from $L$ by taking the intersection of all maximal discrete…

Given an integral domain $D$ and a $D$-algebra $R$, we introduce the local Picard group $\mathrm{LPic}(R,D)$ as the quotient between the Picard group $\mathrm{Pic}(R)$ and the canonical image of $\mathrm{Pic}(D)$ in $\mathrm{Pic}(R)$, and…

We study the set of Dedekind cuts over a linearly ordered Abelian group as a structure over the language (0,<,+,-). Moreover, we obtain a simple set of axioms for the universal part of the theory of such structures. Finally, we prove that…

Let $A$ be an abelian variety with commutative endomorphism algebra over a finite field $k$. The $k$-isogeny class of $A$ is uniquely determined by a Weil polynomial $f_A$ without multiple roots. We give a classification of the groups of…

We study pseudodifferential equations and Riesz kernels attached to certain quadratic forms over p-adic fields. We attach to an elliptic quadratic form of dimension two or four a family of distributions depending on a complex parameter, the…

Given a universal elementary Chevalley-Demazure group $E_\Phi^{sc}(R)$ for which its (standard) parabolic subgroups are finitely generated, we consider the problem of classifying which parabolics $P(R) \subset E_\Phi^{sc}(R)$ are finitely…

In this paper, we present a geometric generalization of class field theory, demonstrating how adelic constructions, central to the spectral realization of zeros of L-functions and the geometric framework for explicit formulas in number…

In his 1951 book "Infinite Abelian Groups", Kaplansky gives a combinatorial characterization of the isomorphism types of embeddings of a cyclic subgroup in a finite abelian group. In this paper we first use partial maps on…

Let $R$ be an integral domain with $qf(R)=K$ and let $F(R)$ be the set of nonzero fractional ideals of $R.$ Call $R$ a dually compact domain (DCD) if for each $I\in F(R)$ the ideal $I_{v}=(I^{-1})^{-1}$ is a finite intersection of principal…

The notion of a topological Jordan decomposition of a compact element of a reductive p-adic group has proven useful in many contexts. In this paper, we generalise it to groups defined over fairly general discretely-valued fields and prove…

We define and study sl\_2-categorifications on abelian categories. We show in particular that there is a self-derived (even homotopy) equivalence categorifying the adjoint action of the simple reflection. We construct categorifications for…

It is shown that every abelian regular Lie group is a quotient of its Lie algebra via the exponential mapping.

We develop the theory of exact completions of regular $\infty$-categories, and show that the $\infty$-categorical exact completion (resp. hypercompletion) of an abelian category recovers the connective half of its bounded (resp. unbounded)…

Greenberg proved that every countable group $A$ is isomorphic to the automorphism group of a Riemann surface, which can be taken to be compact if $A$ is finite. We give a short and explicit algebraic proof of this for finitely generated…

We study deformations of a genus one Riemann surface and of a second order Abelian differential on the surface which preserve the periods of the differential with respect to a chosen canonical homology basis of the surface. We call these…

We investigate the class of root systems $R$ obtained by extending an $A_1$-type irreducible root system by a free abelian group $G$. In this context there is a Weyl group $W$ and a group $U$ with the presentation by conjugation. Both…

Fix an ordinary abelian variety defined over a finite field. The ideal class group of its endomorphism ring acts freely on the set of isogenous varieties with same endomorphism ring, by complex multiplication. Any subgroup of the class…

Let $A$ and $B$ be finite-dimensional simple algebras with arbitrary signature over an algebraically closed field. Suppose $A$ and $B$ are graded by a semigroup $S$ so that the graded identitical relations of $A$ are the same as those of…

Let $\hat\Z_p$ be the ring of $p$-adic integers. We prove in the present paper that the category of polynomial functors from finitely generated free abelian groups to $\hat \Z_p$-modules of degree at most $p$ is equivalent to the category…

In this paper, we consider Abelian varieties over function fields that arise as twists of Abelian varieties by cyclic covers of irreducible quasi-projective varieties. Then, in terms of Prym varieties associated to the cyclic covers, we…