A presentation theorem for smooth projective schemes over discrete valuation rings

Ning Guo; Ivan Panin

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arXiv · 2302.02818

A presentation theorem for smooth projective schemes over discrete valuation rings

Ning Guo·Ivan Panin

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Abstract

In this article, we give a proof for a geometric presentation theorem for any irreducible scheme $X$ smooth projective over a discrete valuation ring $R$. As a consequence, for any reductive $R$-group scheme $\mathbf{G}$, we prove that any generically trivial principal $\mathbf{G}$-bundle over $X$ glued to a principal $\mathbf{G}_U$-bundle over the affine line $\mathbb{A}^1_U$ for a semilocal affine scheme $U$.

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BibTeX RIS

Ning Guo, Ivan Panin. 2023-02-06. A presentation theorem for smooth projective schemes over discrete valuation rings. https://arxiv.org/abs/2302.02818

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