On ℓ-adic Pro-algebraic and Relative Pro-ℓ Fundamental Groups
On ℓ-adic Pro-algebraic and Relative Pro-ℓ Fundamental Groups
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关于 ℓ-adic 亲代数和相对亲ℓ基本群
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发表时间：
2012
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影响因子：
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通讯作者：
J. Pridham
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作者：
J. Pridham
We recall l-adic relative Malcev completions and relative pro-l completions of pro-finite groups and homotopy types. These arise when studying unipotent completions of fibres or of normal subgroups. Several new properties are then established, relating to l-adic analytic moduli and comparisons between relative Malcev and relative pro-l completions. We then summarise known properties of Galois actions on the pro-ℚl-algebraic geometric fundamental group and its big Malcev completions. For smooth varieties in finite characteristics different from l, these groups are determined as Galois representations by cohomology of semisimple local systems. Olsson’s non-abelian etale-crystalline comparison theorem gives slightly weaker results for varieties over l-adic fields, since the non-abelian Hodge filtration cannot be recovered from cohomology.
代数簇同伦群上的伽罗瓦作用
影响因子：
2
作者：
Pridham J
通讯作者：
Pridham J