0
votes
1answer
190 views

Articles about Weil cohomology theory by Grothendieck and Artin

In "The Standard Conjectures" Kleiman says that the following properties of Weil cohomology theory were proved in 1963 for étale cohomology by Artin and Grothendieck, except for the last one that it ...
2
votes
1answer
251 views

Is there any publication of “Beilinson’s dream” on motivic (complexes of) sheaves?

In "Standard conjectures of algebraic cycles" nLab says: "... They were also followed by “Beilinson’s dream” on motivic (complexes of) sheaves which comprise so called standard conjectures of ...
15
votes
1answer
350 views

Is there any publication of Bombieri about the standard conjectures on algebraic cycles?

In "Standard conjectures of algebraic cycles" Grothendieck says: "... These [Standard conjectures] are not really new, and they were worked out about three years ago independently by Bombieri and ...
1
vote
0answers
207 views

Where can I find the article of A. Borel: “Values of zeta-functions at integers, cohomology and polylogarithms”? [closed]

Where on the internet can I find this article? I know that it is in this book: Current trends in mathematics and physics, Narosa, New Delhi, 1995.
5
votes
0answers
59 views

K-Theory and completion [duplicate]

I vaguely remember the existence of a statement that relates the $K$-theory (in the sense of Quillen) of a noetherian local ring $A$ with maximal ideal $\mathfrak{m}$ with the $K$-theory of the ...
8
votes
2answers
458 views

Waldhausen $K$-theory for $G$-spaces

I would guess that the following is true, and that somebody has worked it out, but I don't recall ever seeing it. Can anyone point me to any literature on it? Let $G$ be a finite group. We know that ...
3
votes
2answers
323 views

Morphisms between $K_0$

I suppose this is a question with a well known answer. Suppose $A$ and $B$ are two algebras over some field and there is a map $$ f: \operatorname{K_0}(A) \to \operatorname{K_0}(B) $$ is it ...
2
votes
1answer
374 views

Any abelian category as filtered colimit of categories of projective modules

Recently I have heard somewhere that any (edit: small) abelian category can be expressed as the colimit of categories of projective modules over some rings. The remark was that this is "basically just ...
5
votes
2answers
367 views

Normal subgroups of $SL_2$ of a polynomial ring

What is known about normal subgroups of $SL_2(\mathbb{C}[X])$? Can one hope for a congruence subgroup property, i.e. that every (non-central) normal subgroup contains the kernel of the reduction ...
10
votes
1answer
510 views

K-Theory space of finite abelian groups

Consider the abelian category $\mathsf{finAb}$ of finite abelian groups. It is easy to prove that there is an isomorphism $\mathrm{ord} : K_0(\mathsf{finAb}) \to \mathbb{Q}^+$. Can you give a ...
3
votes
0answers
304 views

K-theory of differential graded modules over differential graded algebras

Suppose you have a smooth vector bundle $E$ over a smooth manifold $X$. If you consider the algebra $ \Omega^\ast (E)$ of differential forms on $E$, it will be homotopy equivalent to the algebra of ...
8
votes
1answer
820 views

Explicit description of boundary map in algebraic K-theory

Recall that for a DVR A with fraction field F and residue field k, there is a "localization" fiber sequence in algebraic K-theory, $$K(k) \rightarrow K(A) \rightarrow K(F).$$ In Remark 5.17 of his ...
7
votes
3answers
2k views

“Must read” papers in algebraic K-theory?

I'm mainly interested (graduate student) in surgery theory and geometric topology. If I have a chance to suggest "must read" papers in geometric topology for beginner, I'm very glad to suggest ...
13
votes
2answers
2k views

What's about “quantum modular forms”?

Do you know where one could read on "Modular Forms, K-theory and Knots"? The combination of themes sounds thrilling! Edit: Zagier's paper on "quantum modular forms" will be published in Clay's ...
4
votes
1answer
292 views

Algebraic K-groups and braids

This is (I think) a reference request: Are there calculations of any algebraic K-groups for the (group ring of) the Artin braid groups?