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20092025
most citedOn Grothendieck--Serre's conjecture concerning principal G-bundles over reductive group schemes:I

13 citations · 34 across the 21 of their papers we have counts for

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math.AG2025

On the generalized Bass--Quillen conjecture in dimension 2

Anastasia Stavrova

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

math.AG2025

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

Philippe Gille, Anastasia Stavrova

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

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.AG2023

On the Gille theorem for the relative projective line

Ivan Panin, Anastasia Stavrova

Let be a Noetherian separated scheme. Let be a reductive -group scheme, and let be a principal -bundle over . We prove that if the restriction of…

math.AG2023★ 1 cited

On the Gille theorem for the relative projective line: I

Ivan Panin, Anastasia Stavrova

We prove a relative version of a theorem on torsors on the projective line due to Philippe Gille. As a consequence we obtain a ``weak homotopy invariance'' result for torsors under…

math.AG2019

Torsors of isotropic reductive groups over Laurent polynomials

Anastasia Stavrova

Let k be a field of characteristic 0. Let G be a reductive group over the ring of Laurent polynomials R=k[x_1^{\pm 1},...,x_n^{\pm 1}]. We prove that G has isotropic rank >=1 over…