Academic Commons

Theses Doctoral

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.


  • thumnail for vanDobbendeBruyn_columbia_0054D_14544.pdf vanDobbendeBruyn_columbia_0054D_14544.pdf application/pdf 823 KB Download File

More About This Work

Academic Units
Thesis Advisors
de Jong, Aise Johan
Ph.D., Columbia University
Published Here
April 13, 2018
Academic Commons provides global access to research and scholarship produced at Columbia University, Barnard College, Teachers College, Union Theological Seminary and Jewish Theological Seminary. Academic Commons is managed by the Columbia University Libraries.