Personal tools
You are here: Home Publications Test ideals via algebras of p-e-linear maps

Test ideals via algebras of p-e-linear maps

Manuel Blickle

Number 60
Author Manuel Blickle
Year 2009
Journal To appear in Journal of Algebraic Geometry

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.

More information about this publication…

Document Actions