Università di Genova（热那亚大学）；Centro de Investigación en Matemáticas（数学研究中心）；BCAM – Basque Center for Applied Mathematics（巴斯克应用数学中心）；Ikerbasque, Basque Foundation for Science（伊卡巴斯科，巴斯克科学基金会）
Alessandro De Stefani, Luis Núñez-Betancourt, Ilya Smirnov
备注：
v3: in v2 and in the published version of the proof of Lemma 4.6, it is claimed that A is Gorenstein. However, in our assumptions one can only say that A is quasi-Gorenstein; this correction does not affect the rest of the proof
Introduced by Takagi and Watanabe, the F-pure threshold is an invariant defined in terms of the Frobenius homomorphism. While it finds applications in various settings, it is primarily used as a local invariant. The purpose of this note is to start filling this gap by opening the study of its behavior on a scheme. To this end, we define the defect of the F-pure threshold of a local ring $(R,\mathfrak{m})$ by setting ${\rm dfpt}(R)=\dim (R) - {\rm fpt}(\mathfrak{m})$. It turns out that this invariant defines an upper semi-continuous function on a scheme and satisfies Bertini-type theorems. We also study the behavior of the defect of the F-pure threshold under flat extensions and after blowing up the maximal ideal of a local ring.
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）
