TY - JOUR

T1 - Rigidity for linear framed presheaves and generalized motivic cohomology theories

AU - Ananyevskiy, Alexey

AU - Druzhinin, Andrei

PY - 2018/7/31

Y1 - 2018/7/31

N2 - A rigidity property for the homotopy invariant stable linear framed presheaves is established. As a consequence a variant of Gabber rigidity theorem is obtained for a cohomology theory representable in the motivic stable homotopy category by a ϕ-torsion spectrum with ϕ∈GW(k) of rank coprime to the (exponential) characteristic of the base field k. It is shown that the values of such cohomology theories at an essentially smooth Henselian ring and its residue field coincide. The result is applicable to cohomology theories representable by n-torsion spectra as well as to the ones representable by η-periodic spectra and spectra related to Witt groups.

AB - A rigidity property for the homotopy invariant stable linear framed presheaves is established. As a consequence a variant of Gabber rigidity theorem is obtained for a cohomology theory representable in the motivic stable homotopy category by a ϕ-torsion spectrum with ϕ∈GW(k) of rank coprime to the (exponential) characteristic of the base field k. It is shown that the values of such cohomology theories at an essentially smooth Henselian ring and its residue field coincide. The result is applicable to cohomology theories representable by n-torsion spectra as well as to the ones representable by η-periodic spectra and spectra related to Witt groups.

KW - Correspondences

KW - Framed correspondences

KW - Motivic homotopy theory

KW - Rigidity

KW - K-THEORY

KW - Motivic hornotopy theory

KW - LOCAL-RINGS

KW - HOMOTOPY-THEORY

UR - http://www.scopus.com/inward/record.url?scp=85047792456&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2018.05.013

DO - 10.1016/j.aim.2018.05.013

M3 - Article

AN - SCOPUS:85047792456

VL - 333

SP - 423

EP - 462

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -