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arXiv · 2603.08061

Serre conjecture II for pseudo-reductive groups

Mac Nam Trung Nguyen
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Abstract

The Serre conjecture II predicts that every torsor under a semisimple, simply connected, algebraic group over a field of cohomological dimension at most 2 and of degree of imperfection at most 1 has a rational point. We generalize this conjecture to pseudo-reductive groups and prove their equivalence. In particular, we show that every torsor under a pseudo-semisimple, simply connected group over a global function field or a non-archimedean local field always has a rational point.

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Mac Nam Trung Nguyen. 2026-03-09. Serre conjecture II for pseudo-reductive groups. https://arxiv.org/abs/2603.08061

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