Alexey Ananyevskiy: Rigidity for framed presheaves and motivic homotopy groups

Coffee: 14.30-15:00

Abstract: We establish a rigidity property for homotopy invariant quasi-stable linear framed presheaves introduced by Garkusha and Panin after Voevodsky. As a consequence we obtain a variant of Gabber rigidity theorem for cohomology theories representable in motivic stable homotopy category by an nh-torsion spectrum, where n is an integer coprime to the charachteristic of the base field and h is the hyperbolic plane in the Grothendieck-Witt ring of the base field. For these cohomology theories we show that the value at an essentially smooth henselian ring and its residue field coincide. The result is applicable to n-torsion spectra as well as spectra related to Witt groups. 
The talk is based on the joint work with Andrei Druzhinin.