Minhyong Kim, The unipotent Albanese map and Selmer varieties for curves

Our main conjecture states an equality between the Frobenius action on the p-adic period and the p-adic absolute CM-period, so we can consider it as a p-adic analogue of Yoshida’s

Moreover, the Homeomorphism Con- jecture gives us a new insight into the theory of the anabelian geometry of curves over algebraically closed fields of characteristic p based on

This research was motivated by Higashiyama’s recent work on the pro-p analogue of the semi-absolute version of the Grothendieck Conjecture for configuration spaces [of dimension ≥

The theorem also implies that all p-adic L-functions for elliptic curves at odd primes p of semi-stable ordinary reductions are integral elements in the Iwasawa algebra.. See

Keywords and Phrases: elliptic curves, p-adic L-functions, Iwa- sawa theory, the Mazur-Tate-Teitelbaum conjecture, exceptional ze- ros, Kato’s element.. One is, as

With regard to Question 2, as a corollary of [30], Theorem F, we prove the following “weak version” of the Grothendieck Conjecture for hyperbolic curves of genus 0 over

Then we have a pro- Σ “group-theoretic” criterion for good reduction of [not necessarily ordinary] hyperbolic curves over p-adic local fields in the following sense: Let C be

surfaces and Mumford curves) of infinite genus which gives $p$ -adic solutions of the. KP hierarchy as in the