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Dominating varieties by liftable ones

van Dobben de Bruyn, Remy

Algebraic geometry in positive characteristic has a quite different flavour than in characteristic zero. Many of the pathologies disappear when a variety admits a lift to characteristic zero. It is known since the sixties that such a lift does not always exist. However, for applications it is sometimes enough to lift a variety dominating the given variety, and it is natural to ask when this is possible.
The main result of this dissertation is the construction of a smooth projective variety over any algebraically closed field of positive characteristic that cannot be dominated by another smooth projective variety admitting a lift to characteristic zero. We also discuss some cases in which a dominating liftable variety does exist.

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More About This Work

Academic Units
Mathematics
Thesis Advisors
de Jong, Aise Johan
Degree
Ph.D., Columbia University
Published Here
April 13, 2018