A variety that cannot be dominated by one that lifts

Remy van Dobben De Bruyn

Research output: Contribution to journalReview articlepeer-review

Abstract

We prove a strong version of a theorem of Siu and Beauville on morphisms to higher genus curves, and we use it to show that if a variety X in characteristic p lifts to characteristic 0, then any morphism X ! C to a curve of genus g ≥ 2 can be lifted along. We use this to construct, for every prime p, a smooth projective surface X over FNp that cannot be rationally dominated by a smooth proper variety Y that lifts to characteristic 0.

Original languageEnglish (US)
Pages (from-to)1-39
Number of pages39
JournalDuke Mathematical Journal
Volume1
Issue number1
DOIs
StatePublished - Apr 1 2021

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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