{"product_id":"espaces-de-berkovich-globaux-categorie-topologie-cohomologie-9783031565038","title":"Espaces de Berkovich Globaux: Catégorie, Topologie, Cohomologie","description":"\u003cp\u003e • Author(s): Thibaud Lemanissier | Jérôme Poineau\u003cbr\u003e • Publisher: Birkhauser\u003cbr\u003e • Publisher Imprint: Birkhauser\u003cbr\u003e • BISAC: Geometry - Algebraic\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eCet 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 \u003ci\u003ep\u003c\/i\u003e-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.\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003eThis 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 \u003ci\u003ep\u003c\/i\u003e-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.\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e","brand":"Atlantic Books","offers":[{"title":"Hardcover","offer_id":46443810291863,"sku":"9783031565038","price":8355.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783031565038.webp?v=1769128096","url":"https:\/\/atlanticbooks.com\/products\/espaces-de-berkovich-globaux-categorie-topologie-cohomologie-9783031565038","provider":"Atlantic Books","version":"1.0","type":"link"}