Abstract
There are two ways to generalise the Brauer group of fields to schemes. The definition of the Brauer group of a field k in terms of central simple algebras over k readily extends to schemes as the group of equivalence classes of Azumaya algebras.
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Colliot-Thélène, JL., Skorobogatov, A.N. (2021). Brauer groups of schemes. 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_3
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DOI: https://doi.org/10.1007/978-3-030-74248-5_3
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