2009/12/31 by Manuel Blickle
Mathematics · #math.AC #math.AG #msc:13A35 #msc:14G17
published as Journal of Algebraic Geometry, 22 (2013), no 1, 49-83 · 29 pages, to appear in Journal of Algebraic Geometry
arxiv created 2011/07/08 · arxiv updated 2013/08/26
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.