preprints and projects
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p-adic Hodge theory of unipotent completions revisited (pdf, arxiv)
Let K/ℚp be a finite extension, and let X/K be an algebraic variety. We present a new proof that the unipotent completion of the geometric étale fundamental group of X is a pro-de Rham representation, and show that it is pro-semi-stable whenever X has semi-stable étale cohomology. We also reprove, using syntomic methods, that it is pro-crystalline at integral base points whenever X admits a smooth proper formal model. All three proofs use the bar construction and are inspired by Wojtkowiak's approach to unipotent fundamental groups.