Related papers: Local Monomialization of Analytic Maps

We prove a comparison theorem between locally analytic group cohomology and Lie algebra cohomology for locally analytic representations of a Lie group over a nonarchimedean field of characteristic 0. The proof is similar to that of…

It is now a classical result that an algebraic space locally of finite type over $\mathbf{C}$ is analytifiable if and only if it is locally separated. In this paper we study non-archimedean analytifications of algebraic spaces. We construct…

This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In three previous papers, we introduce the notion of formal manifolds and study…

We give a new proof of the so-called Lie algebra version of Jacquet-Rallis's fundamental lemma for local non-Archimedean fields of characteristic zero. This proof is local and based on a previous result of W. Zhang on the compatibility of…

We address the question of finding algebraic properties that are respectively equivalent, for a morphism between algebraic varieties over an algebraically closed field of characteristic zero, to be an homeomorphism for the Zariski topology…

We present a non-standard proof of the fact that the existence of a local (i.e. restricted to a point) characteristic-zero, semi-parametric lifting for a variety defined by the zero locus of polynomial equations over the integers is…

We show that the generic automorphism is axiomatisable in the green field of Poizat (once Morleyised) as well as in the bad fields which are obtained by collapsing this green field to finite Morley rank. As a corollary, we obtain "bad…

We prove a characterization for BLD-mappings between locally complete locally compact path-metric spaces. As a corollary we obtain a sharp limit theorem for BLD-mappings.

We use multiplication maps to give a characteristic-free approach to vanishing theorems on toric varieties. Our approach is very elementary but is enough powerful to prove vanishing theorems.

We introduce a local homology theory for linearly compact modules which is in some sense dual to the local cohomology theory of A. Grothendieck. Some basic properties such as the noetherianness, the vanishing and non-vanishing of local…

Suppose that $f: Y\to X$ is a proper, dominant, tamely ramified morphism of algebraic surfaces, over a perfect field. We show that it is possible to perform sequences of monoidal transforms $Y'\to Y$ and $X'\to X$ to obtain an induced…

The Gorenstein property in local algebra admits several characterizations via its module category. The goal of this paper is to collect and generalize such characterizations to the relative setting, i.e., to Gorenstein morphisms as defined…

The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…

In this paper, we study local systems of locally finite associative algebras over fields of characteristic p\ge0. We describe the perfect local systems and study the relation between them and their corresponding locally finite associative…

This is a survey on renormalisation in the locality setup highlighting the role that locality morphisms can play for renormalisation purposes. Having set up a general framework to build regularisation maps, we illustrate renormalisation by…

We prove that every $2$-local automorphism on a finite-dimensional semi-simple Lie algebra $\mathcal{L}$ over an algebraically closed field of characteristic zero is an automorphism. We also show that each finite-dimensional nilpotent Lie…

In this work we prove the local multiplicity at most one theorem underlying the definition and theory of local $\gamma$-, $\epsilon$- and $L$-factors, defined by virtue of the generalized doubling method, over any local field of…

We give a simpler and more conceptual proof that a morphism from a 3-fold to a surface, over an algebraically closed field of characteristic 0, can be made into a toroidal morphism by sequences of blow ups of nonsingular subvarieties above…

In this paper we develop a Morse-like theory in order to decompose birational maps and morphisms of smooth projective varieties defined over a field of characteristic zero into more elementary steps which are locally \'etale isomorphic to…

We give several characterizations of relative homological epimorphisms in the setting of locally convex topological algebras, thereby correcting a gap in our earlier paper [Trans. Moscow Math. Soc. 2008, 27-104].