Frobenius techniques in birational
                    geometry

Patakfalvi, Zsolt

doi:10.1090/pspum/097.1/01683

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“…The following conjecture is called the Weak Ordinarity Conjecture. See [Pat16] for a nice survey on this topic and related matters. Takagi proved that if the Weak Ordinarity Conjecture holds, then log canonical singularities have dense F-pure type: Conjecture 5.3 (Weak ordinarity conjecture).…”

Section: Equicharacteristicmentioning

confidence: 99%

Symbolic Powers of Ideals Defining F-pure and Strongly F-regular Rings

Grifo

Huneke

2017

International Mathematics Research Notices

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Given a radical ideal I in a regular ring R, the Containment Problem of symbolic and ordinary powers of I consists of determining when the containment I (a) ⊆ I b holds. By work of Ein-Lazersfeld-Smith, Hochster-Huneke and Ma-Schwede, there is a uniform answer to this question, but the resulting containments are not necessarily best possible. We show that a conjecture of Harbourne holds when R/I is F-pure, and prove tighter containments in the case when R/I is strongly F-regular.2010 Mathematics Subject Classification. 13A15, 13A35, 13H15.

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Section: Equicharacteristicmentioning

confidence: 99%