Applications and Open Questions
Algebraic K-groups are used in conjectures on special values of L-functions and the formulation of an non-commutative main conjecture of Iwasawa theory and in construction of higher regulators.
Another fundamental conjecture due to Hyman Bass (Bass conjecture) says that all G-groups G(A) (that is to say, K-groups of the category of finitely generated A-modules) are finitely generated when A is a finitely generated Z-algebra.
Read more about this topic: Algebraic K-theory
Famous quotes containing the words open and/or questions:
“The confusion is not my invention. We cannot listen to a conversation for five minutes without being aware of the confusion. It is all around us and our only chance now is to let it in. The only chance of renovation is to open our eyes and see the mess. It is not a mess you can make sense of.”
—Samuel Beckett (1906–1989)
“I can’t quite define my aversion to asking questions of strangers. From snatches of family battles which I have heard drifting up from railway stations and street corners, I gather that there are a great many men who share my dislike for it, as well as an equal number of women who ... believe it to be the solution to most of this world’s problems.”
—Robert Benchley (1889–1945)