The MELODIA Project

Methods for low-dimensional abelian varieties

Deliverables

Samuele Anni, Gaetan Bisson, Annamaria Iezzi, Elisa Lorenzo García, and Benjamin Wesolowski. On the computation of endomorphism rings of abelian surfaces over finite fields. 2025. DOI: 10.48550/ARXIV.2503.08925. URL: https://arxiv.org/abs/2503.08925.

Raymond van Bommel, Jordan Docking, Reynald Lercier, and Elisa Lorenzo García. “Reduction of plane quartics and Dixmier–Ohno invariants”. In: Research in Number Theory 11.1 (Feb. 2025). ISSN: 2363-9555. DOI: 10.1007/s40993-024-00590-x. URL: http://dx.doi.org/10.1007/s40993-024-00590-x.

Jenny Fuselier, Annamaria Iezzi, Mark Kozek, Travis Morrison, and Changningphaabi Namoijam. “Computing supersingular endomorphism rings using inseparable endomorphisms”. In: Journal of Algebra 668 (Apr. 2025), pages 145–189. ISSN: 0021-8693. DOI: 10.1016/j.jalgebra.2025.01.012. URL: http://dx.doi.org/10.1016/j.jalgebra.2025.01.012.

Alexander D. Rahm and Torti Emiliano. “ON THE CALEGARI-VENKATESH CONJECTURE CONNECTING MODULAR FORMS SPACES AND ALGEBRAIC K-THEORY”. working paper or preprint. Mar. 2025. URL: https://hal.science/hal-05014882.

Razvan Barbulescu and Gaetan Bisson. Regev’s attack on hyperelliptic cryptosystems. Cryptology ePrint Archive, Paper 2024/2004. 2024. URL: https://eprint.iacr.org/2024/2004.

Alp Bassa, Gaetan Bisson, and Roger Oyono. “Iterative constructions of irreducible polynomials from isogenies”. In: Finite Fields and Their Applications 97 (Aug. 2024), page 102429. ISSN: 1071-5797. DOI: 10.1016/j.ffa.2024.102429. URL: http://dx.doi.org/10.1016/j.ffa.2024.102429.

Jonas Bergström, Everett W. Howe, Elisa Lorenzo García, and Christophe Ritzenthaler. “Refinements of Katz–Sarnak theory for the number of points on curves over finite fields”. In: Canadian Journal of Mathematics 77.2 (Jan. 2024), pages 400–425. ISSN: 1496-4279. DOI: 10.4153/s0008414x2400004x. URL: http://dx.doi.org/10.4153/S0008414X2400004X.

Andrea Conti and Emiliano Torti. Lattices in rigid analytic representations. 2024. DOI: 10.48550/ARXIV.2403.20232. URL: https://arxiv.org/abs/2403.20232.

Juanita Duque-Rosero, Heidi Goodson, Elisa Lorenzo García, Beth Malmskog, and Renate Scheidler. On invariants of Artin-Schreier curves. 2024. DOI: 10.48550/ARXIV.2401.08843. URL: https://arxiv.org/abs/2401.08843.

Elisa Lorenzo García, Christophe Ritzenthaler, and Fernando Rodríguez Villegas. An arithmetic intersection for squares of elliptic curves with complex multiplication. 2024. DOI: 10.48550/ARXIV.2412.08738. URL: https://arxiv.org/abs/2412.08738.

Samir M. Perlaza, Gaetan Bisson, Iñaki Esnaola, Alain Jean-Marie, and Stefano Rini. “Empirical Risk Minimization With Relative Entropy Regularization”. In: IEEE Transactions on Information Theory 70.7 (July 2024), pages 5122–5161. ISSN: 1557-9654. DOI: 10.1109/tit.2024.3365728. URL: http://dx.doi.org/10.1109/TIT.2024.3365728.

Emiliano Torti. Lagrange’s theorem for a family of finite flat group schemes over local Artin rings. 2024. DOI: 10.48550/ARXIV.2411.12129. URL: https://arxiv.org/abs/2411.12129.

Emiliano Torti. On the existence of analytic families of G-stable lattices and their reductions. 2024. DOI: 10.48550/ARXIV.2401.00462. URL: https://arxiv.org/abs/2401.00462.

Benjamin Wesolowski. “Computing isogenies between finite Drinfeld modules”. In: IACR Communications in Cryptology (Apr. 2024). ISSN: 3006-5496. DOI: 10.62056/avommp-3y. URL: http://dx.doi.org/10.62056/avommp-3y.

Samuele Anni, Eran Assaf, and Elisa Lorenzo García. “On smooth plane models for modular curves of Shimura type”. In: Research in Number Theory 9.2 (Mar. 2023). ISSN: 2363-9555. DOI: 10.1007/s40993-022-00409-7. URL: http://dx.doi.org/10.1007/s40993-022-00409-7.

JONAS BERGSTRÖM, EVERETT W. HOWE, ELISA LORENZO GARCÍA, and CHRISTOPHE RITZENTHALER. “Lower bounds on the maximal number of rational points on curves over finite fields”. In: Mathematical Proceedings of the Cambridge Philosophical Society 176.1 (Sept. 2023), pages 213–238. ISSN: 1469-8064. DOI: 10.1017/s0305004123000476. URL: http://dx.doi.org/10.1017/S0305004123000476.

Raymond van Bommel, Jordan Docking, Vladimir Dokchitser, Reynald Lercier, and Elisa Lorenzo García. Reduction of Plane Quartics and Cayley Octads. 2023. DOI: 10.48550/ARXIV.2309.17381. URL: https://arxiv.org/abs/2309.17381.

Irene Bouw, Nirvana Coppola, Elisa Lorenzo García, and Anna Somoza. On the conductor of Ciani plane quartics. 2023. DOI: 10.48550/ARXIV.2310.10416. URL: https://arxiv.org/abs/2310.10416.

Anh Tuan Bui, Alexander D. Rahm, and Matthias Wendt. “On Farrell–Tate cohomology of GL3 over rings of quadratic integers”. In: Journal of Algebra 615 (Feb. 2023), pages 328–357. ISSN: 0021-8693. DOI: 10.1016/j.jalgebra.2022.09.027. URL: http://dx.doi.org/10.1016/j.jalgebra.2022.09.027.

Luca De Feo, Antonin Leroux, Patrick Longa, and Benjamin Wesolowski. “New Algorithms for the Deuring Correspondence: Towards Practical and Secure SQISign Signatures”. In: Advances in Cryptology – EUROCRYPT 2023. Springer Nature Switzerland, 2023, pages 659–690. ISBN: 9783031305894. DOI: 10.1007/978-3-031-30589-4˙23. URL: http://dx.doi.org/10.1007/978-3-031-30589-4_23.

Linda Frey, Samuel Le Fourn, and Elisa Lorenzo García. Explicit height estimates for CM curves of genus 2. 2023. DOI: 10.48550/ARXIV.2311.13403. URL: https://arxiv.org/abs/2311.13403.

Samir M. Perlaza, Iñaki Esnaola, Gaetan Bisson, and H. Vincent Poor. “On the Validation of Gibbs Algorithms: Training Datasets, Test Datasets and their Aggregation”. In: 2023 IEEE International Symposium on Information Theory (ISIT). IEEE, June 2023, pages 328–333. DOI: 10.1109/isit54713.2023.10206506. URL: http://dx.doi.org/10.1109/ISIT54713.2023.10206506.

Gaetan Bisson and Roger Oyono. “On the vaccination threshold for Covid-19 in French Polynesia”. In: Pacific Health 5 (Aug. 2022). ISSN: 2537-8864. DOI: 10.24135/pacifichealth.v5i.59. URL: http://dx.doi.org/10.24135/pacifichealth.v5i.59.

Eduardo Camps-Moreno, Elisa Gorla, Cristina Landolina, Elisa Lorenzo Garcia, Umberto Martinez-Penas, and Flavio Salizzoni. “Optimal Anticodes, MSRD Codes, and Generalized Weights in the Sum-Rank Metric”. In: IEEE Transactions on Information Theory 68.6 (June 2022), pages 3806–3822. ISSN: 1557-9654. DOI: 10.1109/tit.2022.3156206. URL: http://dx.doi.org/10.1109/TIT.2022.3156206.

Wouter Castryck, Marc Houben, Frederik Vercauteren, and Benjamin Wesolowski. “On the decisional Diffie–Hellman problem for class group actions on oriented elliptic curves”. In: Research in Number Theory 8.4 (Nov. 2022). ISSN: 2363-9555. DOI: 10.1007/s40993-022-00399-6. URL: http://dx.doi.org/10.1007/s40993-022-00399-6.

Sorina Ionica, Pınar Kılıcer, Elisa Lorenzo García, Adelina Mânzățeanu, and Christelle Vincent. Sage module “Bounding denominators of class polynomials for genus 3”. 2022. URL: https://github.com/AdelinaManzateanu/the-embedding-problem.

Samir M. Perlaza, Gaetan Bisson, Inaki Esnaola, Alain Jean-Marie, and Stefano Rini. “Empirical Risk Minimization with Relative Entropy Regularization: Optimality and Sensitivity Analysis”. In: 2022 IEEE International Symposium on Information Theory (ISIT). IEEE, June 2022, pages 684–689. DOI: 10.1109/isit50566.2022.9834273. URL: http://dx.doi.org/10.1109/ISIT50566.2022.9834273.

Benjamin Wesolowski. “Orientations and the Supersingular Endomorphism Ring Problem”. In: Advances in Cryptology – EUROCRYPT 2022. Springer International Publishing, 2022, pages 345–371. ISBN: 9783031070822. DOI: 10.1007/978-3-031-07082-2˙13. URL: http://dx.doi.org/10.1007/978-3-031-07082-2_13.

Benjamin Wesolowski. “The supersingular isogeny path and endomorphism ring problems are equivalent”. In: 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS). IEEE, Feb. 2022, pages 1100–1111. DOI: 10.1109/focs52979.2021.00109. URL: http://dx.doi.org/10.1109/FOCS52979.2021.00109.

Irene Bouw, Nirvana Coppola, Pınar Kılıcer, Sabrina Kunzweiler, Elisa Lorenzo García, and Anna Somoza. Sage module “Reduction type of genus-3 curves in a special stratum of their moduli space”. 2021. URL: https://github.com/NirvanaC93/Invariants-Special-Strata-Genus-3-Curves.