Abstract
In the present paper, it is proved that any complete local domain of mixed characteristic has a weakly almost Cohen–Macaulay algebra $B$ in the sense that a system of parameters is a weakly almost regular sequence in $B$, which is a notion defined via a valuation. In fact, the central idea of this result originates from the main statement obtained by Heitmann to prove the Monomial Conjecture in dimension 3. A weakly almost Cohen–Macaulay algebra is constructed over the absolute integral closure of a complete local domain by applying the methods of Fontaine rings and Witt vectors. A connection of the main theorem with the Monomial Conjecture is also discussed.
Citation
Kazuma Shimomoto. "Almost Cohen–Macaulay algebras in mixed characteristic via Fontaine rings." Illinois J. Math. 55 (1) 107 - 125, Spring 2011. https://doi.org/10.1215/ijm/1355927030
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