Vol. 15, No. 1, 2021

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Torsion orders of Fano hypersurfaces

Stefan Schreieder

Vol. 15 (2021), No. 1, 241–270

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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hypersurfaces, algebraic cycles, unirationality, rationality, unramified cohomology
Mathematical Subject Classification 2010
Primary: 14J70
Secondary: 14C25, 14E08, 14M20
Received: 16 December 2019
Revised: 12 June 2020
Accepted: 21 July 2020
Published: 1 March 2021
Stefan Schreieder
Institute of Algebraic Geometry
Leibniz Universität Hannover