N. Grenier-Boley, M. G. Mahmoudi: Exact Sequences of Witt Groups

grenier@math.univ-fcomte.fr, mahmoudi@math.univ-fcomte.fr

Submission: 2003, Jun 10

An exact octagon of Witt groups of central simple algebras with involution is constructed, extending an exact sequence of Parimala, Sridharan and Suresh and motivated by exact sequences obtained by Lewis. From this, we derive relations between the cardinality of certain Witt groups. An exact octagon of equivariant Witt groups is also obtained, thus generalizing a similar octagon constructed by Lewis for quaternion algebras.

2000 Mathematics Subject Classification: Primary 11E39; Secondary 11E81

Keywords and Phrases: Witt group, hermitian form, central simple algebra with involution, exact sequence of Witt groups, isotropy, equivariant Witt group, Morita equivalence

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