Tate cohomology of special norm modules related to Henselian division algebras
https://doi.org/10.29235/1561-2430-2018-54-3-273-278
Abstract
For central division algebras D over Henselian fields K with unitary K/k-involutions the Tate cohomology groups of Z/(2)-modules A = NZ̅ /K̅(NrdD̅(D̅*)), where K̅ , D̅ are the residue algebras of K and D, respectively, Z̅ is the center of D̅ , and NZ̅ / K̅ is the norm map from Z̅ to K̅ , are computed. Moreover, D is assumed to be tamely ramified K-algebra and a field k̅ belongs either to the class of C1 -fields, or to the class of totally imaginary global fields.
Keywords
Tate cohomology,
Henselian division algebras,
totally imaginary global field,
С1 -field,
reduced norm
Supporting agencies: The Belarusian Republican Foundation for Fundamental Research
About the Author
V. I. Yanchevskiĭ
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Vyacheslav I. Yanchevskiĭ – Member of NAS of Belarus, D. Sc. (Physics and Mathematics), Professor, Head of the Department of Algebra.
11, Surganov Str., 220072, Minsk.
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