We prove the Artin conjecture asserting the finiteness of the Brauer group of an arithmetic model of a smooth projective variety V over a number field k under the assumptions that V admits a k-embedding V ↪ W to a smooth projective hyperkähler ksubvariety \( W\to {\mathbb{P}}_k^N \) such that V = H1 ∩ … ∩ Hr ∩ W in the sense of the theory of schemes for some k-hypersurfaces H1, . . .,Hr in the space \( {\mathbb{P}}_k^N \); moreover, for any i ≤ r the variety H1 ∩ . . . ∩ Hi ∩ W is smooth, has codimension i in the variety W, and dimkV ≥ 3.
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Translated from Problemy Matematicheskogo Analiza 104, 2020, pp. 99-102.
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Prokhorova, T.V. On the Brauer Group of an Arithmetic Model of Strictly Complete Intersection in a HyperkÄhler Variety Over a Number Field. J Math Sci 250, 109–112 (2020). https://doi.org/10.1007/s10958-020-05002-w
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DOI: https://doi.org/10.1007/s10958-020-05002-w