Algebraic geometry

Berkovich space

In mathematics, a Berkovich space, introduced by Berkovich, is a version of an analytic space over a non-Archimedean field (e.g. p-adic field), refining Tate's notion of a rigid analytic space. (Wikipedia).

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The Tempered Topology (on Berkovich Spaces)

This video introduces the tempered topology on Berkovich spaces. These constructions are used to construct Tempered Frobenioids. See Lepage's notes: https://webusers.imj-prg.fr/~emmanuel.lepage/publis/mumfordcurves.pdf

From playlist Geometry of Frobenioids

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Analytic Geometry Over F_1 - Vladimir Berkovich

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From playlist Mathematics

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Andrea Pulita: An overview on some recent results about p-adic differential equations ...

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Complex analytic vanishing cycles for formal schemes - Vladimir Berkovich

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From playlist Mathematics

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Related pages

Field of fractions | Prime ideal | Topological space | Algebraically closed field | Homeomorphism | Zero ring | Ostrowski's theorem | Valuation (algebra) | Empty set | Hausdorff space | Homomorphism | Seminorm | Dense set | Complete field | Rigid analytic space | Mathematics | Set (mathematics) | Integer | Algebraic geometry | Embedding | Ring (mathematics) | Holomorphic function | Compact space | Prime number | Analytic function | Complex number | Interval (mathematics) | Subspace topology | P-adic number