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
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