Modular Symbols and Equivariant Birational Invariants

TL;DR

This paper explores the connections between classical modular symbols for congruence subgroups and the Kontsevich-Pestun-Tschinkel groups linked to finite abelian groups, revealing new relationships in algebraic and geometric structures.

Contribution

It introduces a novel framework relating modular symbols to Kontsevich-Pestun-Tschinkel groups, advancing understanding of their algebraic and geometric properties.

Findings

Established new relations between modular symbols and $ ext{M}_n(G)$ groups.

Provided insights into the structure of equivariant birational invariants.

Connected classical modular symbols with modern algebraic groups.

Abstract

We study relations between the classical modular symbols associated with congruence subgroups and Kontsevich-Pestun-Tschinkel groups $\mathcal{M}_n(G)$ associated with finite abelian groups $G$.