Rigidity for linear framed presheaves and generalized motivic cohomology theories

Alexey Ananyevskiy, Andrei Druzhinin

    Research output: Contribution to journalArticlepeer-review

    1 Scopus citations

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)423-462
    Number of pages40
    JournalAdvances in Mathematics
    Volume333
    DOIs
    StatePublished - 31 Jul 2018

    Scopus subject areas

    • Mathematics(all)

    Keywords

    • Correspondences
    • Framed correspondences
    • Motivic homotopy theory
    • Rigidity
    • K-THEORY
    • Motivic hornotopy theory
    • LOCAL-RINGS
    • HOMOTOPY-THEORY

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