EXACT SEQUENCES OF WITT GROUPS

An exact sequence of Witt groups, motivated by exact sequences obtained by Lewis and by Parimala, Sridharan and Suresh, is constructed. The behavior of the maps involved in these sequences with respect to isotropy is completely determined in the case of division algebras. In particular, the kernels...

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Bibliographic Details
Published inCommunications in algebra Vol. 33; no. 4; pp. 965 - 986
Main Authors Grenier-Boley, N., Mahmoudi, M.G.
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.01.2005
Taylor & Francis
Subjects
Central simple algebra with involution
Equivariant Witt group
Exact sequence of Witt groups
Hermitian form
Isotropy
Mathematics
Morita equivalence
Primary 11E39
Secondary 11E81
Witt group
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Summary:An exact sequence of Witt groups, motivated by exact sequences obtained by Lewis and by Parimala, Sridharan and Suresh, is constructed. The behavior of the maps involved in these sequences with respect to isotropy is completely determined in the case of division algebras. In particular, the kernels of the maps involved in the previous sequences are explicitly given, leading to a new proof of their exactness. Similar exact sequences of equivariant Witt groups are constructed. As an application, relations between the cardinality of certain Witt groups are obtained.
ISSN:0092-7872
1532-4125
DOI:10.1081/AGB-200053791