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Seminar of Algebraic Geometry in East Asia
16:15 - 17:15, April 2, 2021 (Friday)
Zoom, Online seminar
(線上演講 Zoom)
Grothendieck--Serre in the Quasi--split Unramified Case
Kęstutis Česnavičius (Université Paris-Saclay)


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.
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Zoom ID: 466 356 2952



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