二维准自治群体行动的合理性问题

Pub Date : 2024-02-12 DOI:10.1007/s00031-023-09832-1

Akinari Hoshi, Hidetaka Kitayama

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引用次数: 0

摘要

Hoshi, Kang and Kitayama, J. Algebra 403, 363-400, 2014）完全解决了二维纯粹准单数行动的合理性问题。作为推广，我们解决了二维准单子行动的合理性问题，条件是行动定义在基域内。为了证明该定理，我们简要回顾了 Severi-Brauer 变体，并列举了一些例子和合理性结果。我们还使用了非封闭域上\(\mathbb {P}^1\) 的圆锥束的合理性准则。

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Rationality Problem of Two-Dimensional Quasi-Monomial Group Actions

The rationality problem of two-dimensional purely quasi-monomial actions was solved completely by (Hoshi, Kang and Kitayama, J. Algebra 403, 363-400, 2014). As a generalization, we solve the rationality problem of two-dimensional quasi-monomial actions under the condition that the actions are defined within the base field. In order to prove the theorem, we give a brief review of the Severi-Brauer variety with some examples and rationality results. We also use a rationality criterion for conic bundles of \(\mathbb {P}^1\) over non-closed fields.

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