Rigidity theorem for presheaves with Witt-transfers

Druzhinin, A.

doi:10.1090/spmj/1618

Rigidity theorem for presheaves with Witt-transfers
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by A. Druzhinin
Translated by: The author

St. Petersburg Math. J. 31 (2020), 657-673

DOI: https://doi.org/10.1090/spmj/1618

Published electronically: June 11, 2020

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Abstract:

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 $\mathcal F(U)\simeq \mathcal F(x)$ 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 $W^i(-\times Y)$ for any smooth $Y$ over $k$ is obtained, where the $W^i(-)$ 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.

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