The Frobenius action on local cohomology modules in mixed characteristic

Details The Frobenius action on local cohomology modules in mixed characteristic The Frobenius action on local cohomology modules in mixed characteristic

2005-09-27

arxiv.org/abs/math/0509618v2

Mathematics

Commutative Algebra

15 pages, to appear in Compositio Math

Scientific paper

R. Heitmann's proof of the Direct Summand Conjecture has opened a new approach to the study of homological conjectures in mixed characteristic. Inspired by his work and by the methods of almost ring theory, we discuss a normalized length for certain torsion modules, which was introduced by G. Faltings. Using the normalized length and the Frobenius map, we prove some results of local cohomology for local rings in mixed characteristic, which has an immediate implication for the subject of splinters studied by A. Singh.

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