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arXiv · 1804.11158

Corrigendum to N\'eron models, Lie algebras, and reduction of curves of genus one [LLR1] and The Brauer group of a surface [LLR2]

Qing Liu·Dino Lorenzini·Michel Raynaud
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Abstract

Let X be a proper smooth and connected surface over a finite field. We proved in [LLR2] that the order of the Brauer group Br(X) of X is a perfect square if it is finite. Our proof is based in part on a result of Gordon [Gor], which we used in [LLR1] to establish a key formula. Thomas Geisser noted that the formula in [LLR1] is incorrect, due to an omission in [Gor], and provides a corrected formula. We explain in this corrigendum how to modify the work of Gordon to establish a correct formula. The corrected formula can be used to prove the result in [LLR2] without further modifications.

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Qing Liu, Dino Lorenzini, Michel Raynaud. 2018-04-30. Corrigendum to N\'eron models, Lie algebras, and reduction of curves of genus one [LLR1] and The Brauer group of a surface [LLR2]. https://doi.org/10.1007/s00222-018-0809-x

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