Tagged Questions

3
votes
0answers
190 views

“Motivic structure on higher homotopy of non-nilpotent spaces” ?

Has anyone an idea where one can read more about Deepam Patel's talk "Motivic structure on higher homotopy of non-nilpotent spaces" http://www.ihes.fr/~abbes/SGA/patel.html ? Edit …
19
votes
1answer
383 views

What are the possible motivic Galois groups over $\mathbb Q$?

Let $E$ be a motive over $\mathbb Q$. (I should precise, that by a motive I mean here a pure motive over $\mathbb Q$, with coefficients in $\mathbb Q$, that I see here as a conject …
8
votes
2answers
694 views

Status of Beilinson conjectures?

(I hesitate to post that question here, but I received on answer on FB:) Does anyone know how the current status of work on them is? And how the possible generalizations etc. whic …
3
votes
2answers
193 views

critical values of motives

Hi friends, I have some questions concerning the critical values of motives, in the sense of Deligne. I will only look at motives of the form $h^i(X)$ where $X$ is a smooth projec …
4
votes
1answer
266 views

Analogue of Tate or Hodge conjecture for varieties over $\Q_p$

I've been learning about p-adic Hodge theory recently (I'm a beginner), and I've been wondering about the following question the past couple of weeks. Sorry for the long setup, it …
4
votes
1answer
419 views

Should the etale cohomology of a smooth projective variety (over rationals) be semi-simple; why?

$\DeclareMathOperator{\char}{char}\DeclareMathOperator{\gal}{Gal}$ Let $P$ be a smooth projective variety over a field $K$ (one may certainly assume that $K$ is perfect; the case $ …
3
votes
0answers
97 views

Correspondences of schemes induced by a finite Galois extension

I am trying to do the first exercises of the Mazza-Voevodsky-Weibel book Lecture Notes on Motivic Cohomology, which are some elementary results about correspondences between scheme …
1
vote
0answers
63 views

Chow-Künneth decomposition for hypersurfaces

Short version: is the Chow-Künneth motivic decomposition known for $X \hookrightarrow \mathbb{P}^n_k$ a hypersurface over a field $k$? Long version: let $M(X)$ be the Chow motive …
0
votes
1answer
118 views

Pull-back of algebraic cycles under holomorphic maps

Let $f:X \to Y$ be a holomorphic map between two smooth complex projective manifolds. Is there a good notion of pull-back of algebraic cycles by $f$ which preserves degree in the f …
0
votes
1answer
210 views

Realisation functor

Let k be a field. Is there a realization functor $DM_{gm}(k,\mathbb{Z}/n)^{op} \to D^b_c(k, \mathbb{Z}/n)$ from category of motives to category of complexes of étale sheaves of $ …
1
vote
1answer
123 views

Definition of Hurewicz map relating $SH(k)$ with $DM_\_^{eff}(k)$

In "Motivic Homotopy Theory" on page 153 it is stated that there exists a canonical Hurewicz map relating the motivic stable homotopy category with the category $\operatorname{DM}_ …
6
votes
1answer
222 views

Ring structure for the motivic spectrum/complex that represents singular cohomology?

As the discussion here http://mathoverflow.net/questions/42693/is-singular-cohomology-representable-by-a-voevodskys-motivic-complex shows, the singular cohomology of (smooth) compl …
16
votes
1answer
562 views

Grothendieck ring of “varieties carrying a function”

Fix a base ring $R$, and consider pairs $(X,f)$ where $X$ is a scheme of finite type over $R$ and $f:X\to R$ is an $R$-valued algebraic (not constructible!) function on $X$. I wan …
7
votes
0answers
141 views

Corresponding notion of unramified for motives (or de Rham cohomology)

The etale cohomolgoy of a variety $X$ over a number field $K$ is a Galois representation of $\mathrm{Gal}(\overline K/K)$ with some properties coming from $X$, e.g., it is unramifi …
1
vote
0answers
138 views

chow kunneth motivic decomposition for dummies

Hi everybody, I have just realized that, if I had to explain Chow-Kunneth decomposition for Chow motives to someone who is a newbie of the subject, I would hardly find a way which …

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