TY - JOUR

T1 - Rigidity theorem for presheaves with witt-transfers

AU - Druzhinin, A.

N1 - Publisher Copyright: © 2020 American Mathematical Society.

PY - 2020

Y1 - 2020

N2 - The rigidity theorem for homotopy invariant presheaves with Witt-transfers on the category of smooth schemes over a field k of characteristic different form two is proved. Namely, for any such sheaf F, isomorphism F(U) F(x) is established, where U is an essentially smooth local Henselian scheme with a separable residue field over k. As a consequence, the rigidity theorem for the presheaves Wi(-xY) for any smooth Y over k is obtained, where the Wi(-) are derived Witt groups. Note that the result of the work is rigidity with integral coefficients. Other known results are state isomorphisms with finite coefficients.

AB - The rigidity theorem for homotopy invariant presheaves with Witt-transfers on the category of smooth schemes over a field k of characteristic different form two is proved. Namely, for any such sheaf F, isomorphism F(U) F(x) is established, where U is an essentially smooth local Henselian scheme with a separable residue field over k. As a consequence, the rigidity theorem for the presheaves Wi(-xY) for any smooth Y over k is obtained, where the Wi(-) are derived Witt groups. Note that the result of the work is rigidity with integral coefficients. Other known results are state isomorphisms with finite coefficients.

KW - Presheaves with transfers

KW - Rigidity theorem

KW - Witt-correspondences

UR - http://www.scopus.com/inward/record.url?scp=85087563765&partnerID=8YFLogxK

U2 - 10.1090/SPMJ/1618

DO - 10.1090/SPMJ/1618

M3 - Article

AN - SCOPUS:85087563765

VL - 31

SP - 657

EP - 673

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 4

ER -