All Questions
8 questions
3
votes
0
answers
206
views
Generalization of conjectures involving Beilinson regulators
I had some questions about the Beilinson conjectures as mentioned in this page. I have to admit I do not know much about Deligne cohomology. The conjectures involve some form of comparison map between ...
- 5,901
7
votes
1
answer
552
views
Motivation for Suslin’s Rigidity Conjecture
Suslin Rigidity conjecture states that motivic cohomology
$$
H_{\mathcal{M}}^1(\operatorname{Spec}(F),\mathbb{Q}(n))
$$
of the field $F$ coincides with motivic cohomology for the subfield of ...
- 4,316
5
votes
0
answers
513
views
Poincaré duality for motivic cohomology
Is Poincaré duality for étale motivic cohomology known for projective regular (not necessarily smooth, just regular) schemes over Dedekind rings?
More precisely, two questions. Let $f: \mathcal{X}\to\...
user92332
21
votes
1
answer
2k
views
Spectral sequences in $K$-theory
There is an algebraic analogue of the Atiyah-Hirzebruch spectral sequence from singular cohomology to topological $K$-theory of a topological space.
For a field $k$, let $X$ be smooth variety $X$ ...
user87684
17
votes
1
answer
1k
views
Why presheaves with transfer?
Presheaves with transfer are a main technical ingredient in Voevodsky's construction of his category of mixed motives. From the perspective of motivic homotopy theory, the only difference between SH ...
- 171
9
votes
0
answers
1k
views
Motivic cohomology of a point
I was wondering how much is known about the integral motivic cohomology groups of $\mathrm{Spec}\, k$, $H^{n,p}_{\mathrm{mot}}(\mathrm{Spec}\, k,\mathbb{Z})$. One knows that $H^{n,n}_{\mathrm{mot}}(\...
- 596
4
votes
0
answers
218
views
The 'most general' papers on rational Borel-Moore motivic homology and K'-theory?
There are two ways to define Borel-Moore motivic homology (of schemes) with rational coefficients: one should either consider certain complexes of algebraic cycles, or the $\gamma$-filtrations of ...
- 16.9k
12
votes
0
answers
1k
views
Are there analogues of Beilinson's conjectures for motives with coefficients?
There's a body of wisdom (following Beilinson, Bloch, Deligne, ...) relating mixed Tate motives, motivic cohomology, algebraic K-theory, special values of L-functions, and polylogarithms. My ...
- 9,408