Cohomological Obstructions for Varieties over $p$-adic Function Fields

Yisheng Tian

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arXiv · 2606.27699

Cohomological Obstructions for Varieties over $p$-adic Function Fields

Yisheng Tian

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Abstract

We introduce various cohomological obstructions for smooth integral varieties over $p$-adic function fields. We show that the unramified obstruction is the finest one among obstructions arising from arithmetic dualities. We also construct an explicit example whose unramified obstruction gives a proper obstruction while Manin obstruction does not. Finally, we compare the unramified obstruction with the descent obstruction.

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Yisheng Tian. 2026-06-26. Cohomological Obstructions for Varieties over $p$-adic Function Fields. https://arxiv.org/abs/2606.27699

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