Homology of Berkovich spaces

General Introduction
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Online References
arXiv:1211.1422 Singular Homology of nonArchimedean Analytic Spaces and Integration along Cycles fra arXiv Front: math.AG av Tomoki Mihara We constructed new theories on homology of Berkovich's analytic space and integration of an overconvergent differential form along a cycle in the sense of the homology. The new homology satisfies good properties such as what is called the axiom of homology theory, and has the canonical Galois action. The new integration is an extention of Shnirel'man integral, which is the classical integration of an analytic function on the nonArchimedean affine line, and it gives Fontain's padic periods for Tate curves.
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Paper References
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
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Other Information
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