arXiv subjects
Publications and source records attributed to Anastasia Stavrova.
Let G be an isotropic reductive algebraic group over a commutative ring R. Assume that, for any maximal ideal M of R, the rank of the relative root system of G_{R_M} is greater or equal than 2. We show that under this assumption the centralizer of E(R) in G(R) coincides with the abstract group-theoretic center of G(R) and with Cent(G)(R). This generalizes a result of E. Abe and J. Hurley.
Let G be an isotropic reductive algebraic group over a commutative ring R. Assume that the elementary subgroup E(R) of group of points G(R) is correctly defined. Then E(R) is perfect, except for the well-known cases of a split reductive group of type C_2 or G_2.
Let R be a semi-local regular ring containing an infinite perfect field, and let K be the field of fractions of R. Let H be a simple algebraic group of type F_4 over R such that H_K is the automorphism group of a 27-dimensional Jordan algebra which is a first Tits construction. If char K is not 2, this means precisely that the f_3 invariant of H_K is trivial. We prove that if an H-torsor is rationally trivial, then it is trivial over R. This result is a particular case of the Grothendieck-Serre conjecture. It continues the recent series of papers by I. Panin, N.Vavilov and the authors, and complements the result of V. Chernousov on the Grothendieck-Serre conjecture for groups of type F_4 with trivial g_3 invariant.
We prove here some supplementary statements that appeared without proof in I. Panin, A. Stavrova, N. Vavilov, On Grothendieck--Serre's conjecture concerning principal $G$-bundles over reductive group schemes:I, arXiv:0905.1418