(avec C. De Clercq et G. Lucchini-Arteche) Lifting vector bundles to Witt vector bundles, à paraître dans Israel J. Math. [PDF]
(avec D. Izquierdo et G. Lucchini-Arteche) On composition of torsors, 2023, à paraître dans IMRN [PDF]
(avec A. Chapman et K. McKinnie) Common splitting fields of symbol algebras, 2022, Manuscripta Mathematica [PDF]
Realisation of abelian varieties as automorphism groups, 2022, à paraître dans Annales Fac. Sci. Toulouse [PDF]
(avec C. De Clercq) Lifting low-dimensional local systems, 2021, à paraître dans Math. Zeitschrift [PDF]
(avec P. Gille) Residues on affine grassmannians, 2021, à paraître dans Crelle [PDF]
(avec N. Hoffmann et Z. Reichstein) On the rationality problem for forms of moduli spaces of stable marked curves of positive genus, 2020, Ann. SNS di Pisa [PDF]
(avec G. Lucchini-Arteche) On extensions of algebraic groups, 2020, L'Enseignement Math. [PDF]
(avec C. Demarche) Splitting families in Galois cohomology, 2019, Annales Sci. ENS [PDF]
(avec Z. Reichstein) The rationality problem for forms of M_{0,n}, 2018, Bull. London Math. Soc. [PDF]
(avec M. van Garrel) A constructive approach to a conjecture by Voskresenskii, 2018, Selecta Math. [PDF]
(avec D. Anderson et Z. Reichstein) The Lie algebra of type G2 is rational over its quotient by the adjoint action, 2014, Comptes Rendus Acad. Sci. [PDF]
On the symbol length of p-algebras, 2014, Compositio [PDF]
Géométrie birationnelle équivariante des grassmanniennes, 2013, Crelle [PDF]
(avec Bart de Smit et Lara Thomas) The valuation criterion for normal basis generators in unequal characteristic, 2012, Bull. London Math. Soc. [PDF]
On higher trace forms of separable algebras, 2011, Archiv der Math. [PDF]
(avec F. Meunier) Completely symmetric configurations for sigma-games on grid graphs, 2010, Journal of Alg. Combinatorics [PDF]
(avec G. Favi) Tori and essential dimension, 2009, J. of Algebra [PDF]
On the essential dimension of cyclic p-groups, 2008, Inv. Math. [PDF]
Points rationnels sur les espaces homogènes et leurs compactifications, 2005, Trans. Groups
Zéro-cycles de degré un sur les espaces homogènes, 2004, IMRN [PDF]
Liste partielle de prépublications, et autres textes
(avec A. Conti et C. Demarche) Lifting Galois representations via Kummer flags, 2024 [PDF]
(avec U. First et Z. Rosengarten) Torsors that are versal for all affine varieties, 2024 [PDF]
Realisation of linear algebraic groups as automorphism groups, 2023 [PDF]
(avec C. De Clercq) Smooth Profinite Groups, I: Geometrizing Kummer Theory, 2020 [PDF]
(avec C. De Clercq, seconde version) Lifting theorems and smooth profinite groups, 2017 [PDF]
(Réflexions sur la descente; commentaires bienvenus) Multilinear descent theory, 2010 [PDF]
A short proof of Klyachko's theorem about rational algebraic tori, 2006 [PDF]
preprint.
Non rationality of some norm-one tori, 2006 [PDF]
preprint.
Liste partielle d'erreurs ;-)
Smooth Profinite Groups, II: The Uplifting Theorem, 2020 [PDF]
Theorem 14.1 is incorrect. As pointed out by Peter Scholze, the class c, in Step 6 of its proof (Section 16.6), is not geometrically trivial.
In fact, Theorem 14.1 fails even when p=2 and G=C_2 (cyclic group of order 2). However, I believe that Theorem 14.2 is correct.
Today (13/11/2023), I am cheking the new version in detail. I hope to present it soon.
Note that Theorem 14.2 implies that mod p Galois representations (of any field F), lift mod p^2. It also implies Rost-Voevodsky's theorem- see below.
(avec C. De Clercq) Smooth Profinite Groups, III: The Smoothness Theorem, 2020 [PDF]
As written, this text has been checked to be correct, but it relies on Theorem 14.1 of Smooth Profinite Groups, II, which is incorrect- see above.
However, Theorem 14.2 of loc. cit. can be used instead of Theorem 14.1- at the cost of minor changes. The new version of "Smooth Profinite Groups, III" is ready and will be released alongside with II.
(avec C. De Clercq, première version) Smooth profinite groups and applications, 2017 [PDF] As pointed out by Patrick Brosnan, Proposition 11.6 is incorrect. This mistake propagates, in most of remaining contents of the paper.
The current version of this paper is correct, and contains noteworthy constructions. However, as such, we weren't able to deduce from these the liftability of representations of smooth profinite groups, nor to prove Rost-Voevodsky's theorem.
(avec C. De Clercq et G. Lucchini-Arteche, première version) Lifting vector bundles to Witt vector bundles, 2019 [Arxiv]
As pointed out by Alexander Petrov and Barghav Bhatt, Theorem 3.5 is incorrect (in truth, ridiculously optimistic ;-)
The latest version of this text is correct, published, and contains numerous improvements- showcasing the use of Teichmueller lifts of line bundles. "Witt vectors supersede differential calculus®".