PreprintarXiv licencearXiv
Serre's conjectures for Q(√(13))
Abstract
The present article proves (assuming GRH and a minor technical result) the veracity of Serre's conjectures for the field Q(√(13)). In doing so, we prove a ``reduction to level 1'' result that holds for any real quadratic field with narrow class number one. However we can only establish the needed base cases for Q(√(13)).
Related
- Large-time existence for a generalised Serre-Green-Naghdi (Debyaoui-Ersoy) model with variable width and slowly varying bottom
- The unramified Grothendieck--Serre conjecture
- Serre's problem on statistics of Brauer symbols
- On the derived Hall algebra of a graded gentle one-cycle algebra II: Serre presentation
- K-tropical curves, Riemann-Roch and Serre duality
BibTeX
@misc{dieulefait2026serres,
title = {{Serre's conjectures for $\Q(\sqrt13)$}},
author = {Luis Dieulefait and Ariel Pacetti},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38884},
eprint = {2610.38884},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38884},
}
RIS
TY - UNPB
TI - Serre's conjectures for Q(√(13))
AU - Luis Dieulefait
AU - Ariel Pacetti
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38884
UR - https://arxiv.org/abs/2610.38884
AB - The present article proves (assuming GRH and a minor technical result) the veracity of Serre's conjectures for the field Q(√(13)). In doing so, we prove a ``reduction to level 1'' result that holds for any real quadratic field with narrow class number one. However we can only establish the needed base cases for Q(√(13)).
ER -