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- W4312041575 abstract "We prove the weak functoriality of (big) Cohen-Macaulay algebras, which controls the whole skein of homological conjectures in commutative algebra [H1][HH2]. Namely, for any local homomorphism $ Rto R'$ of complete local domains, there exists a compatible homomorphism between some Cohen-Macaulay $R$-algebra and some Cohen-Macaulay $R'$-algebra. When $R$ contains a field, this is already known [[3.9]{HH2}]. When $R$ is of mixed characteristic, our strategy of proof is reminiscent of G. Dietz's refined treatment [D] of weak functoriality of Cohen-Macaulay algebras in characteristic $p$; in fact, developing a tilting argument due to K. Shimomoto, we combine the perfectoid techniques of [A1][A2] with Dietz's result." @default.
- W4312041575 created "2023-01-04" @default.
- W4312041575 creator A5006619634 @default.
- W4312041575 date "2019-11-11" @default.
- W4312041575 modified "2023-09-27" @default.
- W4312041575 title "WEAK FUNCTORIALITY OF COHEN-MACAULAY ALGEBRAS" @default.
- W4312041575 hasPublicationYear "2019" @default.
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