Surjectivity of the total Clifford invariant and Brauer dimension

JOURNAL OF ALGEBRA

卷:443

Article

Auel, Asher

关键词: Quadratic forms;    Line bundle-valued quadratic forms;    Clifford algebras;    Brauer groups;    Brauer dimension;    Classical invariants;    Cohomological invariants;   

DOI  :  10.1016/j.jalgebra.2015.06.043

来源: Elsevier

【 摘 要 】

A celebrated theorem of Merkurjev-that the 2-torsion of the Brauer group is represented by Clifford algebras of quadratic forms-is in general false when the base is no longer a field. The first counterexamples, when the base is among certain arithmetically subtle hyperelliptic curves over local fields, were constructed by Parimala, Scharlau, and Sridharan. We prove that considering Clifford algebras of all line bundle-valued quadratic forms, such counterexamples disappear and we recover Merkurjev's theorem in these cases: for any smooth curve over a local field or any smooth surface over a finite field, the 2-torsion of the Brauer group is always represented by Clifford algebras of line bundle-valued quadratic forms. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free