Talk:Algebraic K-theory
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Crediting the initial theory to Serre rather than Grothendieck is strange and just not true. That Bass defined K1 should be here. Suslin's proof of the Karoubi conjecture showing topological K is a special case of algebraic K should also be here, and the Q construction should be mentioned. Milnor's definition wasn't only for fields.--John Z 16:47, 17 Jun 2005 (UTC)
While I don't know of an explicit counter-example, nor do I have a reference to hand, I'm fairly sure the following statement is incorrect: "When A is a Dedekind domain (e.g. the ring of algebraic integers in an algebraic number field), SK1(A) is zero."
It IS true for the ring of integers in a number field, but not for a general Dedekind domain. In fact, I'm sure I remember reading somewhere that there were even PID's with non-zero SK1, although again I don't know an example. (I believe this is in Rosenberg's Algebraic K-Theory and Its Applications, but like I said i don't have it to hand) 81.76.125.163 22:04, 13 April 2006 (UTC)
[edit] Wrong historical comment removed.
i have just added a sentence about the FACT that grothendieck started the whole theory. Topological K-theory was invented by atiyah and hirzebruch by replacing "algebraic vector bundles by ""topological bundles" in the definition of K_0 by grothendieck. The conjecture of serre on projective modules on polynomial rings, had initially nothing to do with K-theory.
