p-adic iterated integration on semistable curves

Eric Katz; Daniel Litt

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arXiv · 2202.05340

p-adic iterated integration on semistable curves

Eric Katz·Daniel Litt

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Abstract

We reformulate the theory of p-adic iterated integrals on semistable curves using the unipotent log rigid fundamental group. This fundamental group carries Frobenius and monodromy operators whose basic properties are established. By identifying the Frobenius-invariant subgroup of the fundamental group with the fundamental group of the dual graph, we characterize Berkovich--Coleman integration, which is path-dependent, as integration along the Frobenius-invariant lift of a path in the dual graph. Vologodsky's path-independent integration theory which was previously described using a monodromy condition can now be identified as Berkovich--Coleman integration along a combinatorial canonical path arising from the theory of combinatorial iterated integration as developed by the first-named author and Cheng.

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Eric Katz, Daniel Litt. 2022-02-10. p-adic iterated integration on semistable curves. https://arxiv.org/abs/2202.05340

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