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Department of Mathematics,
Department of Mathematics,
University of California San Diego
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Math 209: Number Theory Seminar
Wei Yao
U. Chicago
$p$-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.
[pre-talk at 3pm]
April 1, 2026
4:00 PM
APM 7321
Research Areas
Number Theory****************************
