Related papers: Extension Theorems for Various Weight Functions ov…
We consider linear codes over some fixed finite field extension over an arbitrary finite field. Gabidulin introduced rank metric codes, by endowing linear codes over the extension field with a rank weight over the base field and studied…
We investigate bicomplex analogues of fundamental notions from classical algebraic number theory. In particular, we show that the primitive element theorem admits a natural generalization to bicomplex extensions, giving rise to two distinct…
We study Frobenius eigenvalues of the compactly supported rigid cohomology of a variety defined over a finite field of $q$ elements via Dwork's method. A couple of arithmetic consequences will be drawn from this study. As the first…
We study Galois extensions Coinv(M)<M for M an H-comodule algebra and H a Frobenius Hopf algebroid. We obtain generalizations of various theorems in Hopf-Galois theory by Kreimer-Takeuchi, Doi-Takeuchi and Cohen-Fischman-Montgomery. An…
We classify (up to quasi-isomorphism) the free differential modules whose homology is equal to a given module $M$ by developing a theory for deforming an arbitrary free complex into a differential module. We use an iterative approach to…
We develop a theory of G-dimension for modules over local homomorphisms which encompasses the classical theory of G-dimension for finite modules over local rings. As an application, we prove that a local ring R of characteristic p is…
The aim of this paper is to study two-weight norm inequalities for fractional maximal functions and fractional Bergman operator defined on the upper-half space. Namely, we characterize those pairs of weights for which these maximal…
The aim of this paper is to compute the Frobenius structures of some cohomological operators of arithmetic $\ms{D}$-modules. To do this, we calculate explicitly an isomorphism between canonical sheaves defined abstractly. Using this…
We give sufficient conditions which ensure that a functor of finite length from an additive category to finite-dimensional vector spaces has a projective resolution whose terms are finitely generated. For polynomial functors, we study also…
We present a survey on Weil sums in which an additive character of a finite field $F$ is applied to a binomial whose individual terms (monomials) become permutations of $F$ when regarded as functions. Then we indicate how these Weil sums…
We study the validity of an extension of Frobenius theorem on integral manifolds for some classes of Pfaff-type systems of partial differential equations involving multidimensional "rough" signals, i.e. "differentials" of given H\"older…
We characterize two-weight norm inequalities for potential type integral operators in terms of Sawyer-type testing conditions. Our result is stated in a space of homogeneous type with no additional geometric assumptions, such as group…
In this paper, by using the trace map of Frobenius, we consider problems on extending sections for positive characteristic threefolds.
We investigate criteria for algebra extensions that are of Galois type with respect to the coaction of a Hopf algebra or, more generally, a one-sided quotient of a Hopf algebra, or with respect to an entwining. We study the module- and…
A Type IV-II Z4-code is a self-dual code over Z4 with the property that all Euclidean weights are divisible by eight and all codewords have even Hamming weight. In this paper we use generalized bent functions for a construction of…
This note is devoted to the study of Hyt\"{o}nen's extrapolation theorem of compactness on weighted Lebesgue spaces. Two criteria of compactness of linear operators in the two-weight setting are obtained. As applications, we obtain…
In this paper, we consider the new q-extension of Frobenius-Euler numbers and polynomials and we derive some interesting identities from the orthogonality type properties for the new q-extension of Frobenius-Euler polynomials. Finally we…
Let $\mathfrak g$ be a classical Lie superalgebra of type I or a Cartan-type Lie superalgebra {\bf W}$(n)$. We study weight $\mathfrak g$-modules using a method inspired by Mathieu's classification of the simple weight modules with finite…
We modify the well-known tensor product of modules over a semiring, in order to treat modules over hyperrings, and, more generally, for bimodules (and bimagmas) over monoids. The tensor product of residue hypermodules is functorial. Special…
The purpose of this paper is mostly to present conjectures that extend, to the ``triangular partition'' context (partitions ``under any line'' in the terminology of Blaziak-Haiman-Morse-Pun-Seelinger), properties of Frobenius of…