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adic space

Contents

Contents

Idea

Adic spaces are the basic objects in Huber’s approach to non-archimedean analytic geometry. They are built by gluing valuation spectra? of a certain class of topological rings. Unlike Berkovich analytic spectra the points of adic spaces correspond to valuations of arbitrary rank, not only rank one. If a Berkovich space is corresponding to a separated rigid analytic space then it can be obtained as the largest Hausdorff quotient of the corresponding adic space.

References

  • R. Huber, Étale cohomology of rigid analytic varieties and adic spaces, Aspects of Mathematics, E30. Friedr. Vieweg & Sohn, Braunschweig, 1996. x+450 pp. (MR2001c:14046)

  • Sophie Morel, Adic spaces (pdf)

  • Torsten Wedhorn, Adic spaces (arXiv:1910.05934)

  • Brian Conrad, A brief introduction to adic spaces, PDF.

Last revised on April 27, 2021 at 21:20:42. See the history of this page for a list of all contributions to it.