Jean-Louis Colliot‑Thélène

Jean-Louis Colliot‑Thélène is a French mathematician known for contributions to number theory, algebraic geometry, arithmetic geometry, and algebraic K-theory. He has held research positions at major French institutions and has collaborated with scholars across Europe and North America on problems concerning rational points, the Brauer group, and descent methods. His work connects themes from Alexander Grothendieck's developments in scheme theory to modern approaches influenced by Jean-Pierre Serre, John Tate, and Kazuya Kato.

Early life and education

Born in Paris, Colliot‑Thélène completed his undergraduate studies at the École Normale Supérieure and pursued doctoral work at Université Paris-Sud under mentors active in the French school associated with Alexander Grothendieck and Jean-Pierre Serre. During his formation he engaged with contemporary developments at institutions including the Institut des Hautes Études Scientifiques and attended seminars linked to Bourbaki, Séminaire Chevalley, and research groups influenced by Pierre Deligne and Alexander Merkurjev. His early intellectual milieu involved interaction with researchers from Institut Henri Poincaré, Collège de France, and visiting scholars from Princeton University and Harvard University.

Academic career and positions

Colliot‑Thélène has been affiliated with the Centre National de la Recherche Scientifique (CNRS) and held professorial and research posts at Université Paris-Sud, the Université Paris-Saclay research network, and visiting positions at institutions such as Institut des Hautes Études Scientifiques, École Polytechnique, University of Cambridge, and Princeton University. He participated in collaborative programs at the European Mathematical Society, the International Mathematical Union meetings, and research stays funded by bodies including the Alexander von Humboldt Foundation and the Clay Mathematics Institute. His supervision and collaborations link him to mathematicians from Université de Montréal, University of Chicago, Université Paris 13, and École Normale Supérieure de Lyon.

Research contributions and major results

Colliot‑Thélène's research focuses on rational points on varieties, the arithmetic of algebraic surfaces, the Brauer–Manin obstruction, and cohomological methods in arithmetic geometry. He advanced understanding of the Brauer group in relation to the Hasse principle and formulated conjectures and refined techniques connecting obstruction theories to concrete examples such as del Pezzo surfaces, K3 surfaces, and principal homogeneous spaces under linear algebraic groups like SO and SL_n. His collaborations with Jean-Jacques Sansuc developed descent methods linking Galois cohomology to obstruction phenomena, while joint work with Sir Peter Swinnerton-Dyer and Bjorn Poonen explored rational points over global fields and interactions with étale cohomology. Colliot‑Thélène contributed to results on unramified cohomology, the Bloch–Kato conjecture, and connections to motivic cohomology following lines set by Spencer Bloch, Kazuya Kato, and Vladimir Voevodsky. He investigated zero-cycles and developed criteria for the existence of zero-cycles of degree one on varieties, relating to questions studied by János Kollár, Yuri Manin, and Serge Lang. His influence extends to concrete applications in explicit diophantine problems, interactions with Iwasawa theory perspectives of John Coates, and engagement with arithmetic duality theorems initiated by Jean-Pierre Serre and John Tate.

Awards and honors

He has been recognized by the Centre National de la Recherche Scientifique with distinctions such as the CNRS Silver Medal and received prizes including the Fermat Prize for contributions to number theory and arithmetic geometry. Colliot‑Thélène is a member or fellow of learned bodies and has been invited to speak at major gatherings like the International Congress of Mathematicians, European Congress of Mathematics, and specialist conferences organized by the Mathematical Sciences Research Institute and the Banff International Research Station. He has received visiting fellowships from the Alexander von Humboldt Foundation and research awards connected to the Société Mathématique de France and the Royal Society exchange programs.

Selected publications

- Colliot‑Thélène, J.-L.; Sansuc, J.-J., on descent and the Brauer group for principal homogeneous spaces and rational surfaces; appearing in proceedings associated with Bourbaki seminars and journals tied to the Société Mathématique de France. - Colliot‑Thélène, J.-L.; Sansuc, J.-J.; Swinnerton-Dyer, P., papers on the Hasse principle for del Pezzo surfaces and intersections of quadrics, published in venues connected to Cambridge University Press and leading periodicals affiliated with American Mathematical Society. - Colliot‑Thélène, J.-L.; Sansuc, J.-J.; Soulé, C., works on K-theory and arithmetic related to the Bloch–Kato conjecture and motivic cohomology, appearing in collections honoring Alexander Grothendieck and journals of the European Mathematical Society. - Colliot‑Thélène, J.-L.; Skorobogatov, A.; Swinnerton-Dyer, P., articles on descent, unramified cohomology, and rational points on K3 surfaces and bielliptic varieties, disseminated through conferences at Institut des Hautes Études Scientifiques and proceedings linked to Springer Verlag. - Survey articles and lecture notes by Colliot‑Thélène in volumes published by Cambridge University Press, Springer, and by the Société Mathématique de France covering the Brauer–Manin obstruction, zero-cycles, and arithmetic of linear algebraic groups.

Category:French mathematicians Category:Algebraic geometers Category:Number theorists