• Corpus ID: 11474515

Galois actions on the pro-l-unipotent fundamental group

@article{Pridham2004GaloisAO,
  title={Galois actions on the pro-l-unipotent fundamental group},
  author={Jonathan P. Pridham},
  journal={arXiv: Algebraic Geometry},
  year={2004}
}
  • J. Pridham
  • Published 18 April 2004
  • Mathematics
  • arXiv: Algebraic Geometry
This paper establishes restrictions on the possible Galois actions on the pro-l-unipotent fundamental group of a smooth variety X of good reduction over a local field K. In particular, if X is proper and l is not equal to the residue characteristic p of K, then this action is uniquely determined by the action on cohomology. A similar result for l=p is then proved via a comparison theorem between the crystalline and pro-p homotopy types. 
Galois actions on homotopy groups of algebraic varieties
We study the Galois actions on the l-adic schematic and Artin-Mazur homotopy groups of algebraic varieties. For proper varieties of good reduction over a local field K, we show that the l-adic

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