Related papers: Local factors valued in normal domains

We present a new proof of the classical divergence theorem in bounded domains. Our proof is based on a nonlocal analog of the divergence theorem and a rescaling argument. Main ingredients in the proof are nonlocal versions of the divergence…

The local a priori estimate for the finite element approximation is essential for underlying the local and parallel technique. It is well known that the constant coefficients in the inequality is independent of the mesh size. But it is not…

A theorem is derived which (i) provides a new class of subfactors which may be interpreted as generalized asymptotic subfactors, and which (ii) ensures the existence of two-dimensional local quantum field theories associated with certain…

In this paper local polynomials on Abelian groups are characterized by a "local" Fr\'echet-type functional equation. We apply our result to generalize Montel's Theorem and to obtain Montel-type theorems on commutative groups.

We use former results on geometric local $\varepsilon$-factors over curves in order to prove a factorization result for the determinant of the cohomology of an $\ell$-adic sheaf over an arbitrary proper scheme over a perfect field of…

We develop a theory of integration over valued fields of residue characteristic zero. In particular we obtain new and base-field independent foundations for integration over local fields of large residue characteristic, extending results of…

This is a self-contained purely algebraic treatment of desingularization of fields of fractions $\mathbf{L}:=Q(\mathbf{A})$ of $d$-dimensional domains of the form \[\mathbf{A}:=\bar{\mathbf{F}}[\underline{x}]/\langle…

We estimate the local laws of the distribution of the middle prime factor of an integer, defined according to multiplicity or not. An asymptotic estimate with effective remainder is provided for a wide range of values. In particular this…

In this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new…

Investigating a question of Alladi, we describe the local distribution of small prime factors of integers, with emphasis on the transition phase occurring for certain values of the parameters.

Marc Krasner proposed a theory of limits of local fields in which one relates the extensions of a local field to the extensions of a sequence of related local fields. The key ingredient in his approach was the notion of valued hyperfields,…

Let $K$ be a non-archimedean local field and let $G = \mathrm{GL}_n(K)$. We have shown in previous work that the smooth dual $\mathbf{Irr}(G)$ admits a complex structure: in this article we show how the epsilon factors interface with this…

Let $R$ be a 2-dimensional normal excellent henselian local domain in which 2 is invertible and let $L$ and $k$ be respectively its fraction field and residue field. Let $\Omega_R$ be the set of rank 1 discrete valuations of $L$…

We investigate the renormalization of ``nonlocal'' interactions in an effective field theory using dimensional regularization with minimal subtraction. In a scalar field theory, we write an integro-differential renormalization group…

In the famous paper of Deligne and Mumford, they proved that a proper hyperbolic curve over a discrete valuation field has stable reduction if and only if the Jacobian variety of the curve has stable reduction in the case where the residue…

The chiral space of local fields in Sine-Gordon or the SU(2)-invariant Thirring model is studied as a module over the commutative algebra D of local integrals of motion. Using the recent construction of form factors by means of quantum…

In the probability theory \emph{selfdecomposable, or class $L_0$ distributions} play an important role as they are limiting distributions of normalized partial sums of sequences of independent, not necessarily identically distributed,…

Motivated by DeWitt's viewpoint of covariant field theory, we define a general notion of non-local classical observable that applies to many physical lagrangian systems (with bosonic and fermionic variables), by using methods that are now…

We prove the Bloch-Ogus Theorem for regular local rings geometrically regular over a discrete valuation ring. In particular, we prove the Bloch-Ogus Theorem for regular local rings of mixed characteristic that are essentially smooth over a…

We develop an existence, regularity and potential theory for nonlinear integrodifferential equations involving measure data. The nonlocal elliptic operators considered are possibly degenerate and cover the case of the fractional…