19 pages; v.2: a slight modification of the argument allowed us to extend our results to the case of an arbitrary regular F-finite ring; v.3: final version, to appear in Transactions of the AMS
We continue our study of F-thresholds begun in math/0607660 by an in depth analysis of the hypersurface case. We use the D--module theoretic description of generalized test ideals which allows us to show that in any F--finite regular ring the F-thresholds of hypersurfaces are discrete and rational (in math/0607660 the finite type over a field case was shown for arbitrary ideals). Furthermore we show that any limit of F-pure thresholds of principal ideals in bouneded dimension is again an F-pure-threshold, hence in particular the limit is rational. The study of the set of F-pure-thresholds leads to natural analogs of conjectures of Shokurov and Kollár (for log canonical thresholds) in the case of F-pure-thresholds.
Bounds on the plus-pure thresholds of some hypersurfaces in (ramified) regular rings
Laboratoire de Mathématiques d’Orsay（奥赛数学实验室）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）；Purdue University（普渡大学）；Universidad Autónoma Metropolitana（自治 Metropolitan 大学）；University of Utah（犹他大学）；University of Alabama（阿拉巴马大学）
Diagonal F-thresholds for determinants and Pfaffians
Otto-von-Guericke-University Magdeburg（马格德堡奥托·冯·古里克大学）；University of Notre Dame（圣母大学）；Institute of Mathematics “Simion Stoilow” of the Romanian Academy（罗马尼亚科学院西米翁·斯托伊洛数学研究所）；University of Cassino and Southern Lazio（卡西诺与南拉齐奥大学）；Visvesvaraya National Institute of Technology, Nagpur（那格浦尔维斯瓦纳特国家技术学院）
