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Results tagged with purity
Search options questions only
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user 127776
4
votes
0
answers
410
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Purity for algebraic De Rham complex
Working with varieties over a field $k$ (you can assume it is $\mathbb{C}$ if necessary). Consider the truncated algebraic De Rham complex $\tau^{\leq n}\Omega_X^{\bullet}$ (This is the nice truncatio …
- 5,901
4
votes
1
answer
301
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A question regarding the Suslin's proof on Grayson motivic cohomology
Because of purity (excision) property of the motivic cohomology we have the long exact sequence of the following form(check the paper for more details of the definition of these notations):
$$H^{m+p-1} … Then it is easy to check that $\mathbb{Z}'(n)$ is a homotopy invariant sheaf which satisfies cohomological purity and at weights $\leq 0$ it coincides with the motivic cohomology. …
- 5,901
2
votes
0
answers
77
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Purity of truncated Zariski sheaves of roots of unity
By the purity (excision) for motivic cohmology this implies that for a codimension $c$ closed immersion $f: Z\hookrightarrow X$ of smooth schemes $f^! … I was wondering whether it is possible to show the purity directly and without Quillen-Lichtenbaum? …
- 5,901
3
votes
0
answers
321
views
Relations between the morphic cohomology and Hodge theory
The main question can be summarized in the following form:
For a smooth projective complex variety $X$, is the cohomology $H^{2p}(X, \tau^{\leq p}\Omega_{alg}^{\bullet})$ supposed to surject onto $(H …
- 5,901