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

Abstract

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.

28 pages; v2 minor emendations

References in corpus (4)

• Frobenius Manifolds and Formality of Lie Algebras of Polyvector Fields
• Deformation theory via differential graded Lie algebras
• Deformations via Simplicial Deformation Complexes
• The deformation theory of representations of the fundamental group of a smooth variety

Cited by in corpus (3)

• Deformation of Outer Representations of Galois Group II
• The pro-unipotent radical of the pro-algebraic fundamental group of a compact Kaehler manifold
• Galois actions on the pro-l-unipotent fundamental group