By Vladimir G. Berkovich

The aim of this publication is to introduce a brand new concept of analytic area over a non-Archimedean box. regardless of the whole disconnectedness of the floor box, those analytic areas have the standard topological houses of a posh analytic house, reminiscent of neighborhood compactness and native arcwise connectedness. This makes it attainable to use the standard notions of homotopy and singular homology. The e-book contains a homotopic characterization of the analytic areas linked to convinced periods of algebraic forms and an interpretation of Bruhat-Tits structures by way of those analytic areas. the writer additionally experiences the relationship with the sooner proposal of a inflexible analytic area. Geometrical concerns are used to acquire a few purposes, and the analytic areas are used to build the rules of a non-Archimedean spectral thought of bounded linear operators. This publication calls for a history on the point of easy graduate classes in algebra and topology, in addition to a few familiarity with algebraic geometry. it'd be of curiosity to analyze mathematicians and graduate scholars operating in algebraic geometry, quantity conception, and -adic research.

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