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Rationality in a family

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The Brauer–Grothendieck Group

Abstract

The specialisation method allows one to prove that a smooth and projective complex variety is not stably rational if it can be deformed into a mildly singular variety Z whose desingularisation has a non-zero Brauer group.

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Colliot-Thélène, JL., Skorobogatov, A.N. (2021). Rationality in a family. In: The Brauer–Grothendieck Group. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 71. Springer, Cham. https://doi.org/10.1007/978-3-030-74248-5_12

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