All Questions
Tagged with motivic-cohomology cohomology
7 questions
1
vote
0
answers
136
views
Universal properties for Bloch's higher Chow groups
I work in the category of varieties over some field of characteristic zero. Assume that for any variety I can define the group $\widetilde{CH}^r(X,n)$ which behave like classical Bloch's higher Chow ...
- 219
1
vote
0
answers
213
views
Algebraic correspondence as morphisms in Betti cohomology
$\newcommand{\sing}{\mathrm{sing}}$Take a commutative ring $R$ and smooth projective complex varieties $X$ and $Y$. An element $\alpha\in CH^*(X\times Y)_R$ induces the algebraic correspondence for ...
- 349
6
votes
1
answer
621
views
Representable cohomology theories in motivic homotopy theory
I am reading Mazza's, Voevodsky's and Weibel's book Lecture Notes on Motivic Cohomology and have grown curious about the following question:
Which cohomology theories on $Sm/k$ are representable, i.e. ...
- 133
5
votes
1
answer
488
views
Is $B\mathbb{G}_m$ strongly $A^1$-invariant?
I have just seen the definition of strongly ${A}_1$ invariance:
A sheaf of group $G$ is strongly $A_1$ invariance , if both $H^0(-;G)$ and $H^1(-;G)$ is $A_1$-invariant.
I haven't got too much ...
- 631
1
vote
0
answers
176
views
Differences and relationships between Motivic cohomology and Universal cohomology theory? [duplicate]
Differences and relationships between Motivic cohomology (Beilinson, Lichtenbaum and Voevodsky) and Universal cohomology theory (Grothendieck)?
user56696
2
votes
0
answers
326
views
Voevodsky's 'split standard triple' argument: an explanation; does it work with $Z/nZ$-coefficients?
For varieties over a perfect field (of some characteristic $p$ that could be 0) Voevodsky defines the notion of a 'standard triple' (see http://books.google.ru/books?id=TzUmk87bN9cC&pg=PA85&...
- 16.9k
1
vote
0
answers
232
views
What can one say about a smooth variety whose lower cohomology is trivial?
Let $X$ be a smooth (quasi-affine) complex variety; suppose that its cohomology (say, with integral coefficients) is trivial in degrees $0 < i\le s$ (for some $s>0$). What can one say about such ...
- 16.9k