$p$-adic families of diagonal cycles

TL;DR

This paper constructs a three-variable family of cohomology classes from diagonal cycles on modular curves and establishes a reciprocity law linking it to a triple-product p-adic L-function via Perrin-Riou's regulator.

Contribution

It introduces a new three-variable family of cohomology classes and proves a reciprocity law connecting it to the triple-product p-adic L-function.

Findings

Construction of a three-variable family of cohomology classes.

Proof of a reciprocity law relating classes to p-adic L-function.

Application of Perrin-Riou's regulator in the context.

Abstract

This note provides the construction of a three-variable family of cohomology classes arising from diagonal cycles on a triple product of towers of modular curves, and proves a reciprocity law relating it to the three variable triple-product $p$-adic $L$-function associated to a triple of Hida families by means of Perrin-Riou's $\Lambda$-adic regulator.