Related papers: Flattening and subanalytic sets in rigid analytic …

Let K be an algebraically closed field endowed with a complete non-archimedean norm with valuation ring R. Let f:Y -> X be a map of K-affinoid varieties. In this paper we study the analytic structure of the image f(Y) in X; such an image is…

Let K be an algebraically closed field endowed with a complete non-archimedean norm. Let f:Y -> X be a map of K-affinoid varieties. We prove that for each point x in X, either f is flat at x, or there exists, at least locally around x, a…

To, say, a proper algebraic or holomorphic space $X/S$, and a coherent sheaf ${\mathcal F}$ on $X$ we identify a functorial ideal, the fitted flatifier, blowing up sequentially in which leads to a flattening of the proper transform of…

The purpose of this paper is to define semi- and subanalytic subsets and maps in the context of real analytic orbifolds and to study their basic properties. We prove results analogous to some well-known results in the manifold case. For…

We study the Galois descent of semi-affinoid non-archimedean analytic spaces. These are the non-archimedean analytic spaces which admit an affine special formal scheme as model over a complete discrete valuation ring, such as for example…

Let K be an algebraically closed field of characteristic zero, endowed with a complete nonarchimedean norm. Let X be a K-rigid analytic variety and \Sigma a semianalytic subset of X. Then the closure of \Sigma in X with respect to the…

We give a new proof of the rectilinearization theorem of Hironaka. We deduce rectilinearization as a consequence of our theorem on local monomialization for complex and real analytic morphisms.

The paper deals with Henselian valued field with analytic structure. Actually, we are focused on separated analytic structures, but the results remain valid for strictly convergent analytic ones as well. A classical example of the latter is…

In this thesis we develop the foundations for a theory of analytic geometry over a valued field, uniformly encompassing the case when the base field is equipped with a non-archimedean valuation and the case when it has an archimedean one.…

Let $k$ be a non-archimedean complete field. We prove a substitute for the reduced fiber theorem (of Bosch, L\"utkebohmert and Raynaud) that holds for every morphism $Y\to X$ flat and with geometrically reduced fibers between $k$-affinoid…

We are concerned with rigid analytic geometry in the general setting of Henselian fields $K$ with separated analytic structure, whose theory was developed by Cluckers--Lipshitz--Robinson. It unifies earlier work and approaches of numerous…

In this paper we give a geometric description of the foliation of a generic real analytic family unfolding a real analytic vector field with a weak focus at the origin, and show that two such families are orbitally analytically equivalent…

We call a local homeomorphism $f: (R^n,0)\to(R^n,0)$ blow-analytic if it becomes real analytic after composing with a finite number blowings-up with smooth nowhere dense centers. If the graph of $f$ is semi-algebraic then, by a theorem of…

On a smooth algebraic variety over $\mathbb{C}$, we build the tempered subanalytic and Stein tempered subanalytic sites. We construct the sheaf of holomorphic functions tempered at infinity over these sites and study their relations with…

We define a notion of global analytic space with overconvergent structure sheaf. This gives an analog on a general base Banach ring of Grosse-Kloenne's overconvergent p-adic spaces and of Bambozzi's generalized affinoid varieties over R.…

We prove a monomialization theorem for mappings in general classes of infinitely differentiable functions that are called quasianalytic. Examples include Denjoy-Carleman classes, the class of $\cC^\infty$ functions definable in a…

This text is devoted to the systematic study of relative properties in the context of Berkovich analytic spaces. We first develop a theory of flatness in this setting. After having shown through a counter-example that naive flatness cannot…

I extend the framework of rigid analytic geometry to the setting of algebraic geometry relative to monoids, and study the associated notions of separated, proper, and overconvergent morphisms. The category of affine manifolds embeds as a…

We develop criteria for affine varieties to admit uniruled subvarieties of certain dimensions. The measurements are from long exact sequences of versions of symplectic cohomology, which is a Hamiltonian Floer theory for some open symplectic…

We present a unifying theory of fields with certain classes of analytic functions, called fields with analytic structure. Both real closed fields and Henselian valued fields are considered. For real closed fields with analytic structure,…