Espaces de Berkovich Globaux

Catégorie, Topologie, Cohomologie

Thibaud Lemanissier, Jérôme Poineau

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English

Birkhauser Verlag AG
06 April 2024

Complex analysis, complex variables; Algebraic geometry

Series: Progress in Mathematics

Summary
Details

Cet ouvrage propose une contribution aux fondements de la théorie des espaces de Berkovich globaux. Cette approche récente à la géométrie analytique, qui mêle les théories classiques des espaces analytiques complexes et p-adiques, fournit un cadre géométrique naturel pour plusieurs théories arithmétiques, telle que la théorie d’Arakelov. Les auteurs suivent trois axes principaux, inexplorés au-delà de la dimension 1 : catégorie, topologie et cohomologie. En particulier, ils introduisent une notion de domaine affinoïde surconvergent, pour lequel sont valables les analogues des théorèmes de Tate et de Kiehl.

This monograph contributes to the foundations of the theory of global Berkovich spaces. This recent approach of analytic geometry, which blends the known theories of complex and p-adic analytic spaces, provides a natural geometric framework for several arithmetic theories, such as Arakelov geometry. The authors focus on three main themes which have yet to be investigated beyond dimension 1 : category, topology, and cohomology. In particular, they introduce a notion of overconvergent affinoid domain where the analogues of Tate's and Kiehl's theorems hold.

By: Thibaud Lemanissier, Jérôme Poineau
Imprint: Birkhauser Verlag AG
Country of Publication: Switzerland
Edition: 1�re �d. 2024
Volume: 353
Dimensions: Height: 235mm, Width: 155mm,
ISBN: 9783031565038
ISBN 10: 3031565037
Series: Progress in Mathematics
Pages: 289
Publication Date: 06 April 2024
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active