$p$-adic height pairing using $K_2$-class field theory and Galois-valued heights

Abstract: In this talk, I will construct a $p$-adic height pairing for curves with split degenerate stable reduction over a prime $p$ using the higher class field theory of Kato-Saito. This pairing can be shown to coincide with the standard Coleman-Gross height pairing when extended to the semistable reduction case using methods by Besser and Vologodsky. At the end, I will briefly mention how this new method inspires the definition of a height pairing valued in certain Galois groups related to the function field of the original curve.

number theory

Audience: researchers in the topic

Comments: pre-talk at 3pm

UCSD number theory seminar

Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 3:20pm Pacific) and last about 30 minutes.