Wall crossing in Iwasawa theory

TL;DR

This paper develops a new framework for anticyclotomic Iwasawa theory related to the Gan-Gross-Prasad conjecture, proposing multiple conjectures and proving an abstract Galois cohomology theorem to relate them.

Contribution

It introduces a generalized framework for anticyclotomic Iwasawa theory in the context of unitary groups and the Gan-Gross-Prasad conjecture, extending previous phenomena.

Findings

Proposes multiple main conjectures based on archimedean weight conditions

Establishes an abstract Galois cohomology theorem linking the conjectures

Generalizes phenomena from elliptic curve Iwasawa theory

Abstract

This paper sets up a framework to organize anticyclotomic Iwasawa theory in the context of the Gan-Gross-Prasad conjecture for unitary groups. We propose multiple main conjectures depending on archimedean weight interlacing conditions, generalizing phenomena in the anticyclotomic Iwasawa theory of elliptic curves. We also prove an abstract theorem in Galois cohomology which relates the conjectures.