turkmath.org

Let X be a curve over a p-adic field with semi-stable Reduction and let $\omega$ be a meromorhic 1 form on X. There are two notions of p-adic integration one may associate to this data: the Berkovich Coleman integral which can be performed locally; and the Vologodsky integral with desirable number theoretic properties. In this talk, we present a theorem comparing the two, and describe an algorithm for computing Vologodsky integrals in the case that X is a hyperelliptic curve. We also illustrate our algorithm with a numerical example computed in Sage. This talk is partly based on joint work with Eric Katz.