Torsion orders of Fano hypersurfaces

Schreieder, Stefan

doi:10.2140/ant.2021.15.241

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Torsion orders of Fano hypersurfaces

Stefan Schreieder

Vol. 15 (2021), No. 1, 241–270

DOI: 10.2140/ant.2021.15.241

Abstract

We find new lower bounds on the torsion orders of very general Fano hypersurfaces over (uncountable) fields of arbitrary characteristic. Our results imply that unirational parametrizations of most Fano hypersurfaces need to have very large degree. Our results also hold in characteristic two, where they solve the rationality problem for hypersurfaces under a logarithmic degree bound, thereby extending a previous result of the author from characteristic different from two to arbitrary characteristic.

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Keywords

hypersurfaces, algebraic cycles, unirationality, rationality, unramified cohomology

Mathematical Subject Classification 2010

Primary: 14J70

Secondary: 14C25, 14E08, 14M20

Milestones

Received: 16 December 2019

Revised: 12 June 2020

Accepted: 21 July 2020

Published: 1 March 2021

Authors

Stefan Schreieder
Institute of Algebraic Geometry Leibniz Universität Hannover Hannover Germany

Vol. 15, No. 1, 2021