Abhyankar's perfectoid lemma

DOI10.1007/s10240-017-0096-xzbMath1419.14030OpenAlexW2963015601MaRDI QIDQ1653850

Yves André

Publication date: 7 August 2018

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10240-017-0096-x

zbMATH Keywords

perfectoid spacesalmost purityRiemann extension theoremAbhyankar's lemmaalmost algebra

Mathematics Subject Classification ID

Analytical algebras and rings (13J07) Ramification and extension theory (11S15) Rigid analytic geometry (14G22) Étale and flat extensions; Henselization; Artin approximation (13B40)

Related Items (23)

Big Cohen-Macaulay algebras and the vanishing conjecture for maps of Tor in mixed characteristic ⋮ Closure operations in complete local rings of mixed characteristic ⋮ Integral perfectoid big Cohen-Macaulay algebras via André's theorem ⋮ On the direct summand conjecture and its derived variant ⋮ The direct factor conjecture ⋮ An analogue of adjoint ideals and PLT singularities in mixed characteristic ⋮ Extensions of absolute values on two subfields ⋮ Algebraic geometry in mixed characteristic ⋮ A VARIANT OF PERFECTOID ABHYANKAR’S LEMMA AND ALMOST COHEN–MACAULAY ALGEBRAS ⋮ Cohomological Descent for Faltings Ringed Topos ⋮ Regular rings and perfect(oid) algebras ⋮ Extended plus closure in complete local rings ⋮ Drinfeld's lemma for perfectoid spaces and overconvergence of multivariate \((\varphi, \Gamma)\)-modules ⋮ Finite étale extensions of Tate rings and decompletion of perfectoid algebras ⋮ Purity for the Brauer group ⋮ Finiteness properties and numerical behavior of local cohomology ⋮ Singularities in mixed characteristic. The perfectoid approach ⋮ Singularities and perfectoid geometry ⋮ Singularities in mixed characteristic via perfectoid big Cohen-Macaulay algebras ⋮ Weak functoriality of Cohen-Macaulay algebras ⋮ Another proof of the almost purity theorem for perfectoid valuation rings ⋮ Eliminating tame ramification generalizations of Abhyankar's lemma ⋮ Prisms and prismatic cohomology

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