Diamonds II
This chapter evaluates the complements on the pro-étale topology. It addresses two issues raised in the previous lecture on the pro-étale topology. The first issue concerned descent, or more specifically pro-étale descent for perfectoid spaces. The other issue was that the property of being a pro-étale morphism is not local for the pro-étale topology on the target. The chapter then looks at quasi-pro-étale morphisms, as well as G-torsors. A morphism of perfectoid spaces is quasi-pro-étale if for any strictly totally disconnected perfectoid space with a map, the pullback is pro-étale. Using this definition, one can give an equivalent characterization of diamonds.
1988 ◽
Vol 46
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pp. 830-831
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1982 ◽
Vol 47
(03)
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pp. 197-202
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1975 ◽
Vol 30
(11-12)
◽
pp. 781-784
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