Jumping numbers of F-pure submodules

The objective of this paper is to better understand F-injective thresholds and F-thresholds. Our approach is more general; we investigate the F-pure submodules of a module with a Cartier action, and relate their associated jumping numbers to numerical invariants of a Cartier algebra that resemble F-thresholds. As special cases, we obtain new results on the rationality and m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak {m}}$$\end{document}-adic constancy of F-injective thresholds and F-thresholds.