# Questions tagged [purity]

The purity tag has no usage guidance.

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### Purity of truncated Zariski sheaves of roots of unity

By Quillen-Lichtenbaum theorem the weight $i$ mod $l$ motivic complex is quasi-isomorphic to $\tau^{\leq i}R\alpha_{*}\mu_l^{\otimes i}$ where $\alpha$ is the forgetful functor sending etale sheaves ...

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### A question regarding the Suslin's proof on Grayson motivic cohomology

This question is regarding the proof strategy presented in the paper, "On The Grayson Spectral Sequence", which its overview is explained in page 1 and 2. It seems a very general approach is ...

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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 ...

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### 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^...