Kęstutis Česnavičius - Grothendieck–Serre in the quasi-split unramified case
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 2021-06-08

Correction: The affiliation of Lei Fu is Tsinghua University.

The Grothendieck–Serre conjecture predicts that every generically trivial torsor under a reductive group scheme G over a regular local ring R is trivial. We settle it in the case when G is quasi-split and R is unramified. To overcome obstacles that have so far kept the mixed characteristic case out of reach, we adapt Artin's construction of "good neighborhoods" to the setting where the base is a discrete valuation ring, build equivariant compactifications of tori over higher dimensional bases, and study the geometry of the affine Grassmannian in bad characteristics.