String Two-Point Function = Height Function on a Curve

Abstract

We generalize the recently demonstrated equivalence between local heights and boundary propagators on the Tate curve to any curve over a p-adic local field with semistable reduction. Specifically, we show that the boundary two-point function of a p-adic string theory with the curve as the asymptotic boundary coincides with the Néron local height pairing on degree zero divisors. We remark on the use of AI in this research, see Statement of AI use.