Related papers: A specialization property of index

A variety is a category of ordered (finitary) algebras presented by inequations between terms. We characterize categories enriched over the category of posets which are equivalent to a variety. This is quite analogous to Lawvere's classical…

This text is devoted to the theory of varieties, which provides an important tool, based in universal algebra, for the classification of regular languages. In the introductory section, we present a number of examples that illustrate and…

In the previous papers, Furuta, Yoshida and the author gave a definition of analytic index theory of Dirac-type operator on open manifolds by making use of some geometric structure on an open covering of the end of the open manifold and a…

In this article, we discuss some properties of holomorphic fibrations in the complex analytic setting.

We prove in a unifying way several equivalent descriptions of Koszul rings, some of which being well known in the literature. Most of them are stated in terms of coring theoretical properties of $\Tor_n^A(R,R)$. As an application of these…

In this paper we improve our previous results on classification of groups of points on abelian varieties over finite fields. The classification is given in terms of the Weil polynomial of abelian varieties in a given $k$-isogeny class.

In this paper, we study a particular class of block matrices placing an emphasis on their spectral properties. Some related applications are then presented.

We develop representation theory approach to the study of special functions associated with toric varieties. In particular we show that the corresponding special functions are given by matrix elements of certain non-reductive Lie algebras

Although the characterization of ring derivations has an extensive literature, up to now, all of the characterizations have had the following form: additivity and another property imply that the function in question is a derivation. The aim…

It is investigated how graded variants of integral and complete integral closures behave under coarsening functors and under formation of group algebras.

In this article, some factorization properties of polynomials over discrete valuation domains are elucidated. These properties along with the notion of Newton index of a polynomial leads to a generalization of the main result proved by…

In this paper we will obtain some further properties for specializations in a scheme. Using these results, we will take a picture for a scheme and a picture for a morphism of schemes. In particular, we will prove that every morphism of…

We introduce a notion of secondary characteristic classes of Lie algebra extensions. As a spin-off of our construction we obtain a new proof of Lecomte's generalization of the Chern-Weil homomorphism.

We present a common framework to study varieties in great generality from a categorical point of view. The main application of this study is in the setting of algebraic categories, where we introduce Birkhoff varieties which are essentially…

We examine the topological characteristic cohomology classes of complexified vector bundles. In particular, all the classes coming from the real vector bundles underlying the complexification are determined.

We derive extensions of the monomialization theorems for morphisms of varieties in our earlier work. In this note we show that a local monomialization can be found which satisfies stronger local conditions. Some comments are made about how…

Let $F$ be a global function field of characteristic $p>0$, $K/F$ an $\ell$-adic Lie extension ($\ell\neq p$) and $A/F$ an abelian variety. We provide Euler characteristic formulas for the $Gal(K/F)$-module $Sel_A(K)_\ell$.

This paper is devoted to present some characterizations for a local ring to be generically Gorenstein and Gorenstein by means of $\delta$-invariant and linkage theory.

We give explicit formulae and study the combinatorics of an identity holding in all Rota-Baxter algebras. We describe the specialization of this identity for a couple of examples of Rota-Baxter algebras.

The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.