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PreprintCC BY 4.0HAL

A class formula for effective Anderson motives

  • Xavier Caruso
  • Quentin Gazda
  • Alexis Lucas
Open at sourcePDFDOICite

Abstract

We establish a class formula with variable for arbitrary effective Anderson motives. This pursues the pioneering work of Taelman and extends the scope of the work of Anglès-Ngo Dac-Tavares Ribeiro, removing the admissibility assumption and allowing for more general Anderson modules. In the same setting, we further conjecture a "nondeterminantal" version of the class formula which holds before taking determinants and prove a weak version of it. Finally, we prove an overconvergent version of the class formula and derive from it strong convergence properties for the associated L-series.

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Cite

BibTeXRIS
BibTeX
@misc{caruso2026class,
  title = {{A class formula for effective Anderson motives}},
  author = {Xavier Caruso and Quentin Gazda and Alexis Lucas},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17321},
  eprint = {2609.17321},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05745645v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A class formula for effective Anderson motives
AU  - Xavier Caruso
AU  - Quentin Gazda
AU  - Alexis Lucas
PY  - 2026
DA  - 2026/09/10
PB  - HAL
DO  - 10.48550/arxiv.2609.17321
UR  - https://hal.science/hal-05745645v1
AB  - We establish a class formula with variable for arbitrary effective Anderson motives. This pursues the pioneering work of Taelman and extends the scope of the work of Anglès-Ngo Dac-Tavares Ribeiro, removing the admissibility assumption and allowing for more general Anderson modules. In the same setting, we further conjecture a "nondeterminantal" version of the class formula which holds before taking determinants and prove a weak version of it. Finally, we prove an overconvergent version of the class formula and derive from it strong convergence properties for the associated L-series.
ER  -