The p-adic class numbers of number fields, elliptic curves, knots, and graphs

part 1 – graphs – (30 min) 　by Jun Ueki (Ochanomizu University)
part 2 — number fields, elliptic curves, and knots – (60 min) 　by Hyuga Yoshizaki (Tokyo Science University)
Abstract. Let $p$ be a prime number. As initially pointed out by Sinnott–Han–Kisilevsky and afterward re-discovered by us, in a pro-$p$ extension of number fields or its various analogues, the class number p-adically converges. In a topological setting, the $p$-adic limit value (say, the $p$-adic class number) may be interpreted as Kionke's $p$-adic torsion. We will give numerical observations on this phenomenon and point out further interests, especially in a view of Lang–Trotter conjecture. (This talk is partially based on joint works with Reo Kobayashi and Sohei Tateno.)