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 Miss America contest is ... the most perfectly rendered theater in our culture, for it so perfectly captures what we yearn for: a low-class ritual, a polished restatement of vulgarity, that wants to open the door to high-class respectability by way of plain middle-class anxiety and ambition.”
—Gerald Early (b. 1952)
“There is the falsely mystical view of art that assumes a kind of supernatural inspiration, a possession by universal forces unrelated to questions of power and privilege or the artist’s relation to bread and blood. In this view, the channel of art can only become clogged and misdirected by the artist’s concern with merely temporary and local disturbances. The song is higher than the struggle.”
—Adrienne Rich (b. 1929)