TY - JOUR
T1 - Ascending chain condition for F-pure thresholds on a fixed strongly F-regular germ
AU - Sato, Kenta
N1 - Funding Information:
The author wishes to express his gratitude to his supervisor Professor Shunsuke Takagi for his encouragement, valuable advice and suggestions. The author is also grateful to Professor Mircea Musta¸ta for his helpful comments and suggestions. He would like to thank Doctor Sho Ejiri, Doctor Kentaro Ohno, Doctor Yohsuke Matsuzawa and Professor Hirom Tanaka for useful comments. He is also indebted to the referee for careful reading of the manuscript and thoughtful suggestions. A part of this work was carried out during his visit to University of Michigan with financial support from the Program for Leading Graduate Schools, MEXT, Japan. He was also supported by JSPS KAKENHI 17J04317.
Publisher Copyright:
© 2019 The Author.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - In this paper, we prove that the set of all F-pure thresholds on a fixed germ of a strongly F-regular pair satisfies the ascending chain condition. As a corollary, we verify the ascending chain condition for the set of all F-pure thresholds on smooth varieties or, more generally, on varieties with tame quotient singularities, which is an affirmative answer to a conjecture given by Blickle, Mustaţǎ and Smith.
AB - In this paper, we prove that the set of all F-pure thresholds on a fixed germ of a strongly F-regular pair satisfies the ascending chain condition. As a corollary, we verify the ascending chain condition for the set of all F-pure thresholds on smooth varieties or, more generally, on varieties with tame quotient singularities, which is an affirmative answer to a conjecture given by Blickle, Mustaţǎ and Smith.
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U2 - 10.1112/S0010437X19007358
DO - 10.1112/S0010437X19007358
M3 - Article
AN - SCOPUS:85080906115
SN - 0010-437X
VL - 155
SP - 1194
EP - 1223
JO - Compositio Mathematica
JF - Compositio Mathematica
IS - 6
ER -