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.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/D89K5TB0 |
| Date | January 2018 |
| Creators | van Dobben de Bruyn, Remy |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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