A. Stavrova

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math.AG2025

On the generalized Bass--Quillen conjecture in dimension 2

Anastasia Stavrova

Let $A$ be a regular ring of dimension $\leq 2$ . Let $G$ be a reductive group over $A$ such that its derived group is a split, i.e. a Chevalley--Demazure, semisimple group. We prove…

math.AG2025

Non-Stable $K_{1}$ -Functors of Discrete Valuation Rings Containing a Field

Philippe Gille, Anastasia Stavrova

Let $k$ be a field, and let $G$ be a simply connected semisimple k-group which is isotropic and contains a strictly proper parabolic $k$ -subgroup $P$ . Let $D$ be a discrete valuati…

math.AG2025

R-equivalence on group schemes

Philippe Gille, A Stavrova

We define R-equivalence for group schemes over a semilocal ring and relate this with rational properties. Two main cases are investigated: tori and isotropic semisimple simply conn…

math.AG2025

On a theorem of Harder

Ivan Panin, Anastasia Stavrova

We prove that for any simply connected isotropic reductive group G over a Dedekind domain D, any Zariski-locally trivial principal G-bundle over D is trivial. The corresponding res…

math.AG2025

On the Gille theorem for the relative projective line

Ivan Panin, Anastasia Stavrova

Let $X$ be a Noetherian separated scheme. Let $G$ be a reductive $X$ -group scheme, and let $E$ be a principal $G$ -bundle over $P_{X}^{1}$ . We prove that if the restriction of…

On the generalized Bass--Quillen conjecture in dimension 2

Non-Stable K1​-Functors of Discrete Valuation Rings Containing a Field

R-equivalence on group schemes

On a theorem of Harder

On the Gille theorem for the relative projective line

Non-Stable $K_{1}$ -Functors of Discrete Valuation Rings Containing a Field