Finiteness theorems for the shifted Witt and higher Grothendieck-Witt groups of arithmetic schemes

JOURNAL OF ALGEBRA

卷:351

Article

Jacobson, Jeremy

关键词: Witt groups;    Grothendieck-Witt groups;    Hermitian K-theory;    Arithmetic schemes;    Varieties over finite fields;   

DOI  :  10.1016/j.jalgebra.2011.10.043

来源: Elsevier

【 摘 要 】

For smooth varieties over finite fields, we prove that the shifted (aka derived) Witt groups of surfaces are finite and the higher Grothendieck-Witt groups (aka Hermitian K-theory) of curves are finitely generated. For more general arithmetic schemes, we give conditional results, for example, finite generation of the motivic cohomology groups implies finite generation of the Grothendieck-Witt groups. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free