Karoubi conjecture

Short description: Theorem connecting algebraic and topological K-theories on C* algebras

In mathematics, the Karoubi conjecture is a conjecture by Max Karoubi (1979) that the algebraic and topological K-theories coincide on C* algebras spatially tensored with the algebra of compact operators. It was proved by Andrei Suslin and Mariusz Wodzicki (1990, theorem 6, 1992).

References

• Karoubi, Max (1979), "K-théorie algébrique de certaines algèbres d'opérateurs", in Harpe, Pierre de la, Algèbres d'opérateurs (Sém., Les Plans-sur-Bex, 1978), Lecture Notes in Mathematics, 725, Berlin, New York: Springer-Verlag, pp. 254–290, doi:10.1007/BFb0062621, ISBN 978-3-540-09512-5 
• Suslin, Andrei A.; Wodzicki, Mariusz (1990), "Excision in algebraic K-theory and Karoubi's conjecture", Proceedings of the National Academy of Sciences of the United States of America 87 (24): 9582–9584, doi:10.1073/pnas.87.24.9582, ISSN 0027-8424, PMID 11607130, Bibcode: 1990PNAS...87.9582S 
• Suslin, Andrei A.; Wodzicki, Mariusz (1992), "Excision in algebraic K-theory", Annals of Mathematics, Second Series 136 (1): 51–122, doi:10.2307/2946546, ISSN 0003-486X