Vol. 3, No. 4, 2021

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Descent for nonarchimedean analytic spaces

Brian Conrad and Michael Temkin

Vol. 3 (2021), No. 4, 689–748

We study two types of descent in the category of Berkovich analytic spaces: flat descent and descent with respect to an extension of the ground field. Quite surprisingly, the deepest results in this direction seem to be of the second type, including the descent of properties of being a good analytic space and being a morphism without boundary.

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nonarchimedean geometry, Berkovich spaces, descent
Mathematical Subject Classification
Primary: 14G22
Secondary: 14D15
Received: 4 June 2020
Revised: 2 March 2021
Accepted: 17 March 2021
Published: 20 October 2021
Brian Conrad
Department of Mathematics
Stanford University
United States
Michael Temkin
Einstein Institute of Mathematics
The Hebrew University of Jerusalem