18 citations · 59 across the 11 of their papers we have counts for
10 papers · 1 filter
Non-Archimedean volumes of metrized nef line bundles
Sébastien Boucksom, Walter Gubler, Florent Martin
Let be a line bundle on a proper, geometrically reduced scheme over a non-trivially valued non-Archimedean field . Roughly speaking, the non-Archimedean volume of a cont…
Differentiability of relative volumes over an arbitrary non-Archimedean field
Sébastien Boucksom, Walter Gubler, Florent Martin
Given an ample line bundle on a geometrically reduced projective scheme defined over an arbitrary non-Archimedean field, we establish a differentiability property for the relat…
Continuity of Plurisubharmonic Envelopes in Non-Archimedean Geometry and Test Ideals (with an Appendix by José Ignacio Burgos Gil and Martín Sombra)
Walter Gubler, Philipp Jell, Klaus Künnemann +1
Let L be an ample line bundle on a smooth projective variety X over a non-archimedean field K. For a continuous metric on L, we show in the following two cases that the semipositiv…
On Zhang's semipositive metrics
Walter Gubler, Florent Martin
Zhang introduced semipositive metrics on a line bundle of a proper variety. In this paper, we generalize such metrics for a line bundle of a paracompact strictly -analytic s…
Differentiability of non-archimedean volumes and non-archimedean Monge-Ampère equations (with an appendix by Robert Lazarsfeld)
José Ignacio Burgos Gil, Walter Gubler, Philipp Jell +2
Let be a normal projective variety over a complete discretely valued field and a line bundle on . We denote by the analytification of in the sense of…
Analytic functions on tubes of non-Archimedean analytic spaces
Florent Martin, Christian Kappen
Let be a discretely valued non-Archimedean field. We give an explicit description of analytic functions whose norm is bounded by a given real number on tubes of reduced …
A definable, p-adic analogue of Kirszbraun's Theorem on extensions of Lipschitz maps
Raf Cluckers, Florent Martin
A direct application of Zorn's Lemma gives that every Lipschitz map has an extension to a Lipschitz map $\widetilde f: \mathbb{Q}_p…
Dimensions in non-Archimedean geometries
Florent Martin
Let be an algebraically closed non-Archimedean field. Leonard Lipshitz has introduced a manageable notion of subanalytic sets of the unit polydisc. This class contains the clas…
Overconvergent subanalytic subsets in the framework of Berkovich spaces
Florent Martin
We study the class of overconvergent subanalytic subsets of a -affinoid space when is a non-archimedean field. These are the images along the projection $X \times B^n \t…
Cohomology of locally-closed semi-algebraic subsets
Florent Martin
Let k be a non archimedean field. If X is a k-algebraic variety and U a locally closed semi-algebraic subset of X^{an} -- the Berkovich space associated to X -- we show that for l…