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Potentially stably rational conic bundles over nonclosed fields

Published 28 Oct 2024 in math.AG | (2410.21436v2)

Abstract: We study stable rationality of conic bundles $X$ over $\mathbb{P}1$ defined over non-closed field $k$ via the cohomology of the Galois group of finite field extension $k'/k$ with action on the geometric Picard lattice of $X$.

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