An overview of abelian varieties in homotopy theory

TL;DR

This paper provides an expository overview of formal group laws in homotopy theory, emphasizing their connections to higher-dimensional abelian varieties and automorphic forms, bridging algebraic geometry and topology.

Contribution

It offers a comprehensive exposition linking formal group laws in homotopy theory to higher-dimensional abelian varieties and automorphic forms, highlighting new interdisciplinary connections.

Findings

Clarifies the role of formal group laws in homotopy theory

Explores connections to higher-dimensional abelian varieties

Discusses implications for automorphic forms

Abstract

This is an expository article on the theory of formal group laws in homotopy theory, with the goal of leading to the connection with higher-dimensional abelian varieties and automorphic forms. These are roughly based on a talk at the conference "New Topological Contexts for Galois Theory and Algebraic Geometry."