By Antoine Ducros,Charles Favre,Johannes Nicaise
We current an creation to Berkovich’s idea of non-archimedean analytic areas that emphasizes its functions in quite a few fields. the 1st half comprises surveys of a foundational nature, together with an advent to Berkovich analytic areas by means of M. Temkin, and to étale cohomology by way of A. Ducros, in addition to a brief observe by means of C. Favre at the topology of a few Berkovich areas. the second one half makes a speciality of purposes to geometry. A moment textual content through A. Ducros includes a new evidence of the truth that the better direct photos of a coherent sheaf less than a formal map are coherent, and B. Rémy, A. Thuillier and A. Werner offer an outline in their paintings at the compactification of Bruhat-Tits structures utilizing Berkovich analytic geometry. The 3rd and ultimate half explores the connection among non-archimedean geometry and dynamics. A contribution by means of M. Jonsson encompasses a thorough dialogue of non-archimedean dynamical platforms in measurement 1 and a couple of. eventually a survey by means of J.-P. Otal provides an account of Morgan-Shalen's thought of compactification of personality varieties.
This ebook will give you the reader with adequate fabric at the easy suggestions and buildings regarding Berkovich areas to maneuver directly to extra complicated examine articles at the topic. We additionally desire that the purposes awarded the following will motivate the reader to find new settings the place those attractive and complex items may arise.
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Berkovich Spaces and Applications (Lecture Notes in Mathematics) by Antoine Ducros,Charles Favre,Johannes Nicaise