$p$-adic Beilinson conjecture for ordinary Hecke motives associated to imaginary quadratic fields

TL;DR

This paper reviews a series of works on the $p$-adic Beilinson conjecture related to motives from Hecke characters of imaginary quadratic fields, focusing on primes that split in the field.

Contribution

It provides an overview of recent progress on the $p$-adic Beilinson conjecture for Hecke motives associated with imaginary quadratic fields, highlighting key developments.

Findings

Progress on $p$-adic Beilinson conjecture for split primes in imaginary quadratic fields

Development of techniques for motives associated to Hecke characters

Enhanced understanding of $p$-adic $L$-functions in this context

Abstract

The purpose of this article is to give an overview of the series of papers [BK1], [BK2] concerning the $p$-adic Beilinson conjecture of motives associated to Hecke characters of an imaginary quadratic field $K$, for a prime $p$ which splits in $K$.