Special Groups, Versality and the Grothendieck-Serre Conjecture

  • Zinovy Reichstein

    Department of Mathematics, University of British Columbia, Vancouver, BC V6R1Z2, Canada
  • Dajano Tossici

    Univ. Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F-33400 Talence, France
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Abstract

Let be a base field and be an algebraic group over . J.-P. Serre defined to be special if every -torsor is locally trivial in the Zariski topology for every reduced algebraic variety defined over . In recent papers an a priori weaker condition is used: is called special if every -torsor is split for every field  containing . We show that these two definitions are equivalent. We also generalize this fact and propose a strengthened version of the Grothendieck-Serre conjecture based on the notion of essential dimension.

Cite this article

Zinovy Reichstein, Dajano Tossici, Special Groups, Versality and the Grothendieck-Serre Conjecture. Doc. Math. 25 (2020), pp. 171–188

DOI 10.4171/DM/743