A variety that cannot be dominated by one that lifts

Remy van Dobben De Bruyn

doi:10.1215/00127094-2020-0055

A variety that cannot be dominated by one that lifts

Remy van Dobben De Bruyn

Mathematics

Research output: Contribution to journal › Review article › peer-review

2 Scopus citations

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 F^N_p that cannot be rationally dominated by a smooth proper variety Y that lifts to characteristic 0.

Original language	English (US)
Pages (from-to)	1251-1289
Number of pages	39
Journal	Duke Mathematical Journal
Volume	170
Issue number	7
DOIs	https://doi.org/10.1215/00127094-2020-0055
State	Published - Apr 1 2021

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1215/00127094-2020-0055

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AB - 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.

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A variety that cannot be dominated by one that lifts

Abstract

All Science Journal Classification (ASJC) codes

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