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PreprintCC BY 4.0HAL

Endogenies and linearization in the non-virtually connected case

  • Moreno Invitti
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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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Cite

BibTeXRIS
BibTeX
@misc{invitti2026endogenies,
  title = {{Endogenies and linearization in the non-virtually connected case}},
  author = {Moreno Invitti},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  eprint = {2511.07058},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05338417v3},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Endogenies and linearization in the non-virtually connected case
AU  - Moreno Invitti
PY  - 2026
DA  - 2026/09/04
PB  - HAL
UR  - https://hal.science/hal-05338417v3
AB  - 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.
ER  -