F-rationality mod p implies rationality in mixed characteristic and characteristic zero

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Event details

Date 20.09.2017
Hour 15:3016:30
Speaker Karl Schwede (University of Utah)
Location
MA A1 10
Category Conferences - Seminars

In her thesis, Karen Smith showed that if a variety in characteristic zero had the property that its mod p reductions were F-rational for some p >> 0, then R had rational singularities in characteristic zero.

Suppose now that R is a local ring in mixed characteristic.  Suppose that R/p has F-rational singularities for some p.  We prove that R then has rational singularities in mixed characteristic and hence any localization to characteristic 0 also has rational singularities.  We also will discuss various generalizations to this statement.

This is joint work with Linquan Ma and uses recent advances in our understanding of singularities in mixed characteristic.

Practical information

  • Informed public
  • Free

Organizer

  • Zsolt Patakfalvi

Contact

  • Monique Kiener

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