By Vladimir G. Berkovich
The aim of this booklet is to introduce a brand new suggestion of analytic area over a non-Archimedean box. regardless of the complete disconnectedness of the floor box, those analytic areas have the standard topological houses of a posh analytic house, equivalent to neighborhood compactness and native arcwise connectedness. This makes it attainable to use the standard notions of homotopy and singular homology. The ebook contains a homotopic characterization of the analytic areas linked to convinced periods of algebraic kinds and an interpretation of Bruhat-Tits structures when it comes to those analytic areas. the writer additionally experiences the relationship with the sooner idea of a inflexible analytic house. Geometrical issues are used to procure a few purposes, and the analytic areas are used to build the principles of a non-Archimedean spectral thought of bounded linear operators. This ebook calls for a historical past on the point of simple graduate classes in algebra and topology, in addition to a few familiarity with algebraic geometry. it might be of curiosity to analyze mathematicians and graduate scholars operating in algebraic geometry, quantity thought, and -adic research.
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