Open Access
VOL. 74 | 2017 The weak ordinarity conjecture and $F$-singularities
Bhargav Bhatt, Karl Schwede, Shunsuke Takagi

Editor(s) Keiji Oguiso, Caucher Birkar, Shihoko Ishii, Shigeharu Takayama

Adv. Stud. Pure Math., 2017: 11-39 (2017) DOI: 10.2969/aspm/07410011


Recently M. Mustaţă and V. Srinivas related a natural conjecture about the Frobenius action on the cohomology of the structure sheaf after reduction to characteristic $p \gt 0$ with another conjecture connecting multiplier ideals and test ideals. We generalize this relation to the case of singular ambient varieties. Additionally, we connect these results to a conjecture relating $F$-injective and Du Bois singularities. Finally, using an unpublished result of Gabber, we also show that $F$-injective and Du Bois singularities have a common definition in terms of smooth hypercovers.


Published: 1 January 2017
First available in Project Euclid: 23 October 2018

zbMATH: 1390.14060
MathSciNet: MR3791207

Digital Object Identifier: 10.2969/aspm/07410011

Primary: 13A35 , 14B05 , 14F18 , 14F20 , 14J17

Keywords: $F$-injective , Du Bois , multiplier ideal , ordinary variety , test ideal

Rights: Copyright © 2017 Mathematical Society of Japan


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