2022/02/10 by Eric Katz, Daniel Litt, Katz, Eric +1
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Topological and Geometric Data Analysis #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2202.05340
openalex publication_date 2022/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.