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Presented By: Student Algebraic Geometry Seminar - Department of Mathematics

Student Algebraic Geometry: From rigid analytic spaces to adic spaces

Beomseok Kwon

In Math 731, we studied Berkovich analytic spaces, which are analogues of complex analytic spaces over non-archimedean fields. In this talk, we will explore other approaches to non-archimedean geometry. Tate was the first to successfully develop a form of non-archimedean geometry. Here, the basic objects of study are rigid analytic spaces. These are obtained by gluing maximal spectra of affinoid algebras endowed with Grothendieck topologies. However, rigid spaces are deficient in points, so several refinements have evolved. Raynaud treats a rigid analytic space as the generic fiber of a formal model over the valuation ring. Huber's adic space associated to a rigid analytic space can be thought of as the limit of all formal models. If time permits, we will also discuss cohomology of rigid analytic spaces.

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