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Stably irrational hypersurfaces of small slopes


Author: Stefan Schreieder
Journal: J. Amer. Math. Soc. 32 (2019), 1171-1199
MSC (2010): Primary 14J70, 14E08; Secondary 14M20, 14C30
DOI: https://doi.org/10.1090/jams/928
Published electronically: August 1, 2019
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Abstract: Let $ k$ be an uncountable field of characteristic different from two. We show that a very general hypersurface $ X\subset \mathbb{P}^{N+1}_k$ of dimension $ N\geq 3$ and degree at least $ \log _2N +2$ is not stably rational over the algebraic closure of $ k$.


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Additional Information

Stefan Schreieder
Affiliation: Mathematisches Institut, LMU München, Theresienstr. 39, 80333 München, Germany
Email: schreieder@math.lmu.de

DOI: https://doi.org/10.1090/jams/928
Keywords: Hypersurfaces, rationality problem, stable rationality, integral Hodge conjecture, unramified cohomology.
Received by editor(s): February 14, 2018
Received by editor(s) in revised form: September 10, 2018, April 27, 2019, April 30, 2019, and May 23, 2019
Published electronically: August 1, 2019
Article copyright: © Copyright 2019 American Mathematical Society