Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2025

On the Calegari-Venkatesh conjecture connecting modular forms spaces and algebraic K-Theory

Résumé

Calegari and Venkatesh did construct, modulo small torsion, a surjection from the degree 2 homology of the rank 2 projective general linear group over a ring of algebraic integers (of odd class number, and with enough embeddings) to the 2nd algebraic K-group of that ring. They asked whether this surjection becomes an isomorphism when passing to the quotient modulo the Eisenstein ideal on the left hand side. We provide a new method (together with numerical examples) to lift elements in the opposite direction, enabled by a theorem in a more general setting, where we exploit a connection between the algebraic K-groups and the Steinberg homology groups.

Fichier principal
Vignette du fichier
Rahm_and_Torti.pdf (223.91 Ko) Télécharger le fichier

Dates et versions

hal-05014882 , version 1 (31-03-2025)
hal-05014882 , version 2 (14-04-2025)
hal-05014882 , version 3 (22-10-2025)

Licence

Identifiants

  • HAL Id : hal-05014882 , version 3

Citer

Alexander D. Rahm, Torti Emiliano. On the Calegari-Venkatesh conjecture connecting modular forms spaces and algebraic K-Theory. 2025. ⟨hal-05014882v3⟩

Collections

189 Consultations
494 Téléchargements

Partager

  • More