Dominating varieties by liftable ones
By: Remy van Dobben de Bruyn
Publisher: [publisher not identified]
Published: 2018
Place of publication: [New York, N.Y.?]
Language: eng
Description: 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.
Notes: Department: Mathematics.

Thesis advisor: Aise Johan de Jong.

Thesis (Ph.D.)--Columbia University, 2018.