The structure of the pro-l-unipotent fundamental group of a smooth variety

Details The structure of the pro-l-unipotent fundamental group of a smooth variety The structure of the pro-l-unipotent fundamental group of a smooth variety

2004-01-27

arxiv.org/abs/math/0401378v2

Mathematics

Algebraic Geometry

28 pages; v2 minor emendations

Scientific paper

By developing a theory of deformations over nilpotent Lie algebras, based on Schlessinger's deformation theory over Artinian rings, this paper investigates the pro-l-unipotent fundamental group of a variety X. If X is smooth and proper, defined over a finite field, then the Weil conjectures imply that this group is quadratically presented. If X is smooth and non-proper, then the group is defined by equations of bracket length at most four.

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