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4 papers
Weight filtrations on Selmer schemes and the effective Chabauty--Kim method
L. Alexander Betts
We develop an effective version of the Chabauty--Kim method which gives explicit upper bounds on the number of -integral points on a hyperbolic curve in terms of dimensions of c…
Semisimplicity and weight-monodromy for fundamental groups
L. Alexander Betts, Daniel Litt
Let X be a smooth, geometrically connected variety over a p-adic local field. We show that the pro-unipotent fundamental group of X (in both the etale and crystalline settings) sat…
The local theory of unipotent Kummer maps and refined Selmer schemes
L. Alexander Betts, Netan Dogra
We study the Galois action on paths in the -pro-unipotent étale fundamental groupoid of a hyperbolic curve over a -adic field with . We prove an…
Variation of Tamagawa numbers of Jacobians of hyperelliptic curves with semistable reduction
L. Alexander Betts
We study how Tamagawa numbers of Jacobians of hyperelliptic curves vary as one varies the base field or the curve, in the case of semistable reduction. We find that there are stron…