On the First Galois Cohomology Group of the Algebraic Group SL1(D) |
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Authors: | R Hazrat |
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Institution: | 1. Max Planck Institute in Mathematics , Bonn, Germany;2. Department of Pure Mathematics , Queen's University , Belfast, UK r.hazrat@qub.ac.uk |
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Abstract: | Let A be a central simple algebra over a field F. Denote the reduced norm of A over F by Nrd: A* → F* and its kernel by SL1(A). For a field extension K of F, we study the first Galois Cohomology group H 1(K,SL1(A)) by two methods, valuation theory for division algebras and K-theory. We shall show that this group fails to be stable under purely transcendental extension and formal Laurent series. |
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Keywords: | Central simple algebras Reduced K-theory Reduced norm Valuation theory |
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