Deligne's freeness conjecture for the graded Galois Lie algebra of the thrice-punctured projective line
Deligne's freeness conjecture for the graded Galois Lie algebra of the thrice-punctured projective line
Let be the thrice-punctured projective line over , let be its absolute Galois group, and let denote the associated graded Lie algebra for the relevant -adic filtration. Let the Soule elements be the distinguished graded elements arising from the Galois action. Deligne's conjecture. The graded Lie algebra
is a free graded Lie algebra over generated by the Soule elements, and its Lie algebra structure is induced from a Lie algebra over independent of . This predicts an -independent, freely generated structure for the graded Lie algebra governing the outer Galois representation of the fundamental group of the thrice-punctured projective line; the supplied text does not state a resolution.
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Primary source
Arash Rastegar, “Deformation of Outer Representations of Galois Group”, arXiv:math/0405351 (2006).
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