Test ideals via algebras of $p^{-e}$-linear maps

Details Test ideals via algebras of $p^{-e}$-linear maps Test ideals via algebras of $p^{-e}$-linear maps

2009-12-11

arxiv.org/abs/0912.2255v3

Mathematics

Commutative Algebra

29 pages, to appear in Journal of Algebraic Geometry

Scientific paper

Continuing ideas of a recent preprint of Schwede arXiv:0906.4313 we study test ideals by viewing them as minimal objects in a certain class of $F$-pure modules over algebras of p^{-e}-linear operators. This shift in the viewpoint leads to a simplified and generalized treatment, also allowing us to define test ideals in non-reduced settings. In combining this with an observation of Anderson on the contracting property of p^{-e}-linear operators we obtain an elementary approach to test ideals in the case of affine k-algebras, where k is an F-finite field. It also yields a short and completely elementary proof of the discreteness of their jumping numbers extending most cases where the discreteness of jumping numbers was shown in arXiv:0906.4679.

Affiliated with

Also associated with

No associations

Rating

Test ideals via algebras of $p^{-e}$-linear maps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Test ideals via algebras of $p^{-e}$-linear maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Test ideals via algebras of $p^{-e}$-linear maps will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-468526