A generalization of the Ross symbols in higher K-groups and hypergeometric functions II

TL;DR

This paper extends the concept of Ross symbols to higher K-groups and hypergeometric functions, providing a p-adic perspective and applying it to the p-adic Beilinson conjecture for specific K3 surfaces.

Contribution

It introduces a p-adic analogue of higher Ross symbols and applies this to the p-adic Beilinson conjecture for K3 surfaces with maximal Picard number.

Findings

Development of p-adic Ross symbols

Application to p-adic Beilinson conjecture for K3 surfaces

Advancement in understanding hypergeometric functions in higher K-theory

Abstract

This is a sequel of the paper "A generalization of the Ross symbols in higher K-groups and hypergeometric functions I" where we introduced higher Ross symbols in higher $K$-groups of the hypergeometric schemes, and discussed the Beilinson regulators. In this paper we give its p-adic counterpart and an application to the $p$-adic Beilinson conjecture for K3 surfaces of Picard number 20.