Research

Publications

1. (with Giancarlo Lucchini Arteche) Transfer principles for Galois cohomology and Serre's conjecture II, preprint, 2023. Version on Arxiv.
2. (with Mathieu Florence and Giancarlo Lucchini Arteche) On composition of torsors, International Mathematics Research Notices, vol 2023(19), p. 16930–16956, 2023. Published version.
3. (with Giancarlo Lucchini Arteche) On Kato and Kuzumaki's properties for the Milnor K₂ of function fields of p-adic curves, accepted in Algebra and Number Theory, 2023. Version on arXiv.
4. La aritmética de las ecuaciones con muchas variables, Gaceta de la Real Sociedad Matemática Española, Vol. 24(1), p. 161-183, 2021. Published version.
5. (with Giancarlo Lucchini Arteche) Local-global principles for homogeneous spaces over some two-dimensional geometric global fields, Journal für die reine und angewandte Mathematik (Crelle), vol. 2021(781), p. 165-186, 2021. Published version.
6. Autour de la conjecture de Milnor, Gazette SMF, Vol. 166, 2020. Published version. And a complement with the proof of theorem 8.6: Complément à un article de la Gazette des Mathématiciens sur la conjecture de Milnor.
7. (with Auguste Hébert and Benoît Loisel) Lambda-buildings associated to quasi-split groups over Lambda-valued fields, accepted in Münster Journal of Mathematics, 2024. Version on arXiv.
8. (with Giancarlo Lucchini Arteche) Homogeneous spaces, algebraic K-theory and cohomological dimension of fields, Journal of the European Mathematical Society, Vol. 24(6), p. 2169–2189, 2022. Published version.
9. Vanishing theorems and Brauer-Hasse-Noether exact sequences for the cohomology of higher-dimensional fields, Transactions of the AMS, Vol. 372, p. 8621-8662, 2019. Published version.
10. (with David Harari) L'espace adélique d'un tore sur un corps de fonctions, Annales de l'Institut Fourier, Vol. 69(5), p. 1915-1954, 2019. Published version.
11. On a conjecture of Kato and Kuzumaki, Algebra and Number Theory, Vol. 12(2), p. 429–454, 2018. Published version.
12. Dualité et principe local-global pour les anneaux locaux henséliens de dimension 2, with an appendix by Joël Riou, Algebraic Geometry, Vol. 6(2), p. 148-176, 2019. Published version.
13. Variétés abéliennes sur les corps de fonctions de courbes sur des corps locaux, Documenta Mathematica, Vol. 22, p. 297-361, 2017. Published version.
14. Dualité pour les groupes de type multiplicatif sur certains corps de fonctions , Comptes Rendus de l'Académie des Sciences, Vol. 355(3), p. 268-271, 2017. Published version.
15. Principe local-global pour les corps de fonctions sur des corps locaux supérieurs II , Bulletin de la SMF, Vol. 145(2), p. 267-293, 2017. Published version.
16. Théorèmes de dualité pour les corps de fonctions sur des corps locaux supérieurs , Mathematische Zeitschrift, Vol. 284(1-2), p. 615-642, 2016. Published version.
17. Principe local-global pour les corps de fonctions sur des corps locaux supérieurs I, Journal of Number Theory, Vol 157, p.250-270, Dec. 2015. Published version.

Contributions to conference proceedings

• Duality and local-global principle over two-dimensional henselian local rings, in Quadratic Forms and Related Structures over Fields, Oberwolfach reports 21/2018, European Mathematical Society.

Posters

• On a conjecture of Kato and Kuzumaki, poster for the conference Arithmétique, Géométrie et Représentations at the University Paris 6 in October 2017.

Academic texts

• Habilitation à diriger des recherches, defended on December 1st, 2021. Defense committee: Philippe Gille, David Harbater, Raman Parimala, Bjorn Poonen, Bertrand Rémy (referee), Tamás Szamuely (referee) and Olivier Wittenberg (referee). Video and slides of the defense.
• (under the supervision of David Harari) The manuscript of my Ph.D. thesis , defended in October 2016. Defense committee: Jean-Louis Colliot-Thélène (chairman of the committee), David Harari (Ph.D. advisor), Bruno Kahn, Cédric Pépin, Alexei Skorobogatov, Tamás Szamuely. Here are the slides of the defense.
• (under the supervision of David Harari) Le théorème de Poitou-Tate, an introduction to the Poitou-Tate theorem, September 2013.
• (under the supervision of David Harari) Le théorème de Poitou-Tate à partir du théorème d'Artin-Verdier, short thesis on Artin-Verdier duality and Poitou-Tate duality, June 2013.
• (under the supervision of Florian Herzig) Conjecture de Serre pour des représentations modérément ramifiées de dimension 3 du groupe de Galois d'un corps CM , Master thesis, University of Toronto, December 2012.
• (avec Yichao Huang, under the supervision of Olivier Wittenberg) Le problème de Noether pour les groupes abéliens, Bachelor thesis, École normale supérieure (Paris), June 2011.

Seminars and conferences

Rational Varieties seminar

With Charles De Clercq and Cyril Demarche, I currently organize the Rational Varieties seminar in Paris.

GAAAAG

With Zhizhong Huang, I organized a small workshop on arithmetic geometry on July 1^st and 2^nd 2020: Geometric, Algebraic and Analytic Approches to Arithmetic Geometry.