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Algebraic K-Theory and Galois Cohomology

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First European Congress of Mathematics Paris, July 6–10, 1992

Part of the book series: Progress in Mathematics ((PM,volume 120))

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Abstract

The present paper contains some results and conjectures concerning the relations between the algebraic K-theory of rings and Galois cohomology theory. The first part of this paper is devoted to fields, and the second part to simple algebras of finite dimension over the center. In the interaction between algebraic K-theory and Galois cohomology theory, both of them exert influence on one another. For example, the problem whether the Brauer group of a field is generated by the classes of cyclic algebras was raised long before the algebraic K-theory was constructed, but it plays a crucial role in the solution of the problem. On the other hand, Galois cohomology theory can explain some phenomena in the algebraic K-theory (indecomposable group K 3, SK 1 for certain simple algebras).

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Author information

Authors and Affiliations

  1. Department of Mathematics and Mechanics, Bibliotechnaya 2, Petrodvorets, Saint-Petersburg, 198904, Russia

    Alexander S. Merkurjev

Authors
  1. Alexander S. Merkurjev
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Editor information

Editors and Affiliations

  1. Laboratoire de Mathématiques Fondamentales, Université Pierre et Marie Curie, 4, place Jussieu, 75252, Paris Cedex 05, France

    Anthony Joseph  & Rudolf Rentschler  & 

  2. The Weizmann Institute of Science, Rehovot, 76100, Israel

    Anthony Joseph

  3. Mathématiques, Université de Paris-Sud, Bâtiment 425, 91405, Orsay Cedex, France

    Fulbert Mignot

  4. Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie, 4, place Jussieu, 75252, Paris Cedex 05, France

    François Murat

  5. Laboratoire de Statistique Médicale, Université Paris V, 45, rue des Saints Pères, 75270, Paris Cedex 06, France

    Bernard Prum

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© 1994 Birkhäuser Verlag

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Merkurjev, A.S. (1994). Algebraic K-Theory and Galois Cohomology. In: Joseph, A., Mignot, F., Murat, F., Prum, B., Rentschler, R. (eds) First European Congress of Mathematics Paris, July 6–10, 1992. Progress in Mathematics, vol 120. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9112-7_10

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  • DOI: https://doi.org/10.1007/978-3-0348-9112-7_10

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9912-3

  • Online ISBN: 978-3-0348-9112-7

  • eBook Packages: Springer Book Archive

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