Karoubi conjecture

In mathematics, the Karoubi conjecture is a conjecture by 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 Suslin and 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 Math., 725, Berlin, New York: Springer-Verlag, pp. 254–290, doi:10.1007/BFb0062621, MR 548119 
• 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, JSTOR 2356456, MR 1081504 
• 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, MR 1173926