On integrality of $p$-adic iterated integrals

TL;DR

This paper proves integrality properties of certain $p$-adic iterated Coleman integrals on curves with good reduction, leading to bounds on valuations of $p$-adic multiple zeta values.

Contribution

It establishes integrality results for $p$-adic iterated Coleman integrals on specific algebraic curves, a novel contribution to $p$-adic number theory and arithmetic geometry.

Findings

Proves integrality of specific $p$-adic iterated integrals.

Provides a lower bound for valuations of $p$-adic multiple zeta values.

Applies to curves with good reduction, including the projective line and elliptic curves.

Abstract

The purpose of this paper is to prove integrality for certain $p$-adic iterated Coleman integrals. As underlying geometry we will take the complement of a divisor $D\subset X$ with good reduction, where $X$ is the projective line or an elliptic curve over the Witt vectors of a perfect characteristic $p$ field. As a corollary we prove a lower bound for the valuations of $p$-adic multiple zeta values.