PreprintarXiv licencearXiv
Computing the cohomology of Shimura curves in quasi-linear time
Abstract
Computing spaces of modular and automorphic forms is an important problem in algorithmic number theory, with in particular Diophantine applications to generalised Fermat and other equations. The case of Shimura curves was studied by Greenberg and Voight by cohomological methods, allowing them to reduce the problem to linear algebra. Relying on work of Imbert, we leverage topological techniques to obtain linear systems so structured that they can be solved in time quasi-linear in the genus.
Related
- Igusa stacks and the cohomology of Shimura varieties
- Modular and Shimura curves X0D(N) embedded in ℙ1 × ℙ1
- Shimura curves of discriminant 14 and 15 and associated Heun Functions
- Arithmetic duality for p -adic pro-étale cohomology of analytic curves
- Stable rational cohomology splitting of moduli of branched covers of curves
BibTeX
@misc{bait2026computing,
title = {{Computing the cohomology of Shimura curves in quasi-linear time}},
author = {Rayane Baït and Aurel Page},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29209},
eprint = {2609.29209},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29209},
}
RIS
TY - UNPB
TI - Computing the cohomology of Shimura curves in quasi-linear time
AU - Rayane Baït
AU - Aurel Page
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29209
UR - https://arxiv.org/abs/2609.29209
AB - Computing spaces of modular and automorphic forms is an important problem in algorithmic number theory, with in particular Diophantine applications to generalised Fermat and other equations. The case of Shimura curves was studied by Greenberg and Voight by cohomological methods, allowing them to reduce the problem to linear algebra. Relying on work of Imbert, we leverage topological techniques to obtain linear systems so structured that they can be solved in time quasi-linear in the genus.
ER -