Test ideals via algebras of $p^{-e}$-linear maps
Abstract
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 -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.
Cite
@article{arxiv.0912.2255,
title = {Test ideals via algebras of $p^{-e}$-linear maps},
author = {Manuel Blickle},
journal= {arXiv preprint arXiv:0912.2255},
year = {2013}
}
Comments
29 pages, to appear in Journal of Algebraic Geometry