Opendata, web and dolomites

TOSSIBERG SIGNED

Theory of Stein Spaces in Berkovich Geometry

Total Cost €

0

EC-Contrib. €

0

Partnership

0

Views

0

Project "TOSSIBERG" data sheet

The following table provides information about the project.

Coordinator
UNIVERSITE DE CAEN NORMANDIE 

Organization address
address: ESPLANADE DE LA PAIX
city: CAEN CEDEX 5
postcode: 14032
website: www.unicaen.fr

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country France [FR]
 Project website https://poineau.users.lmno.cnrs.fr/TOSSIBERG.html
 Total cost 1˙153˙750 €
 EC max contribution 1˙153˙750 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-STG
 Funding Scheme ERC-STG
 Starting year 2015
 Duration (year-month-day) from 2015-07-01   to  2020-06-30

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITE DE CAEN NORMANDIE FR (CAEN CEDEX 5) coordinator 1˙153˙750.00

Map

 Project objective

Complex Stein spaces may be thought of as analytic analogues of the affine schemes of algebraic geometry. They may be characterized in several manners: using convergence of holomorphic functions, topological properties or potential-theoretic properties, for instance. Especially useful for applications is the fact that their coherent cohomology vanishes. Despite the crucial importance of this theory in complex analytic geometry, its p-adic counterpart has hardly been sketched. In the setting of Berkovich geometry (one among the several notions of p-adic geometry), recent developments have enabled to get a fine understanding of the topology of the spaces (work of Berkovich and Hrushovski-Loeser) and to define the basic tools of potential theory (work of Baker-Rumely, Thuillier, Boucksom-Favre-Jonsson and Chambert-Loir-Ducros). The conditions for a comprehensive study of p-adic Stein spaces are now met; this will be our first goal. The theory will then be used to investigate envelopes of holomorphy and meromorphy. As an application, I plan to derive rationality criteria for power series over function fields. The second part of the project is devoted to the theory of Stein spaces for Berkovich spaces over rings of integers of number fields (where all the places appear on an equal footing). Those spaces have hardly been studied and only a very small part of the usual analytic machinery is available in this setting. Here, my main goal will consist in proving the basic and fundamental fact that relative polydisks are Stein spaces (in the cohomological sense). This will allow a deeper investigation of rings of convergent arithmetic power series (i.e. with integral coefficients) and will lead up to properties related to commutative algebra but also to the inverse Galois problem. Knowing that the coherent cohomology of polydisks vanishes also opens the road towards computing global cohomology groups for projective analytic spaces over ring of integers of number fields.

 Publications

year authors and title journal last update
List of publications.
2019 Pablo Cubides Kovacsics, Jinhe Ye
Tame pairs, Definable types and Pro-definability
published pages: , ISSN: , DOI:
2020-04-23
2018 Pablo Cubides Kovacsics, Deirdre Haskell
Real closed valued fields with analytic structure
published pages: , ISSN: , DOI:
2020-04-23
2019 Lorenzo Fantini, Daniele Turchetti
Triangulations of non-archimedean curves, semi-stable reduction, and ramification
published pages: , ISSN: , DOI:
2020-04-23
2019 Pablo Cubides Kovacsics, Jérôme Poineau
DEFINABLE SETS OF BERKOVICH CURVES
published pages: 1-65, ISSN: 1474-7480, DOI: 10.1017/S1474748019000495
Journal of the Institute of Mathematics of Jussieu 2020-04-23
2017 Saskia Chambille, Pablo Cubides Kovacsics, Eva Leenknegt
Clustered cell decomposition in P -minimal structures
published pages: 2050-2086, ISSN: 0168-0072, DOI: 10.1016/j.apal.2017.06.002
Annals of Pure and Applied Logic 168/11 2020-04-23
2017 PABLO CUBIDES KOVACSICS, KIEN HUU NGUYEN
A P-MINIMAL STRUCTURE WITHOUT DEFINABLE SKOLEM FUNCTIONS
published pages: 778-786, ISSN: 0022-4812, DOI: 10.1017/jsl.2016.58
The Journal of Symbolic Logic 82/02 2020-04-23
2018 Lorenzo Fantini, Daniele Turchetti
Galois descent of semi-affinoid spaces
published pages: , ISSN: 0025-5874, DOI: 10.1007/s00209-018-2054-9
Mathematische Zeitschrift 2020-04-23
2017 Velibor Bojkovic, Jérôme Poineau
Pushforwards of p-adic differential equations
published pages: , ISSN: , DOI:
2020-04-23
2017 Pablo Cubides Kovacsics
A proof of Liouville’s theorem via o-minimality
published pages: , ISSN: , DOI:
2020-04-23
2017 Vlerë Mehmeti
Patching over Berkovich Curves and Quadratic Forms
published pages: , ISSN: , DOI:
2020-04-23
2017 Marco Maculan, Jérôme Poineau
Notions of Stein spaces in non-archimedean geometry
published pages: , ISSN: , DOI:
2020-04-23
2017 Pablo Cubides Kovacsics, Françoise Point, Quentin Brouette
Strong density of definable types and closed ordered differential fields
published pages: , ISSN: , DOI:
2020-04-23
2018 Saskia Chambille, Pablo Cubides Kovacsics, Eva Leenknegt
Exponential-constructible functions in P-minimal structures
published pages: , ISSN: , DOI:
2020-04-23
2018 Pablo Cubides Kovacsics, Françoise Delon
Definable functions in tame expansions of algebraically closed valued fields
published pages: , ISSN: , DOI:
2020-04-23
2018 Velibor Bojković, Jérôme Poineau
On the number of connected components of the ramification locus of a morphism of Berkovich curves
published pages: , ISSN: 0025-5831, DOI: 10.1007/s00208-018-1668-x
Mathematische Annalen 2020-04-23
2018 Anna Blaszczok, Pablo Cubides Kovacsics, Franz-Viktor Kuhlmann
On valuation independence and defectless extensions of valued fields
published pages: , ISSN: , DOI:
2020-04-23

Are you the coordinator (or a participant) of this project? Plaese send me more information about the "TOSSIBERG" project.

For instance: the website url (it has not provided by EU-opendata yet), the logo, a more detailed description of the project (in plain text as a rtf file or a word file), some pictures (as picture files, not embedded into any word file), twitter account, linkedin page, etc.

Send me an  email (fabio@fabiodisconzi.com) and I put them in your project's page as son as possible.

Thanks. And then put a link of this page into your project's website.

The information about "TOSSIBERG" are provided by the European Opendata Portal: CORDIS opendata.

More projects from the same programme (H2020-EU.1.1.)

PROGRESS (2019)

The Enemy of the Good: Towards a Theory of Moral Progress

Read More  

DISINTEGRATION (2019)

The Mass Politics of Disintegration

Read More  

SUExp (2018)

Strategic Uncertainty: An Experimental Investigation

Read More