Endogenies and linearization in the non-virtually connected case

2025/11/10 by Moreno Invitti, Invitti, Moreno
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2511.07058

openalex created_date 2025/11/02 · openalex publication_date 2025/11/10 · openalex updated_date 2026/07/28

Abstract

We prove a linearization theorem for pre-rings of endogenies acting on a definable abelian group of finite dimension. Observe that no assumptions on the connectivity of A are made. We also prove a similar result when one of the two pre-rings is of quasi-endomorphisms. A corollary of these results is a generalization of Zilber's Field Theorem for finite-dimensional theories.

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