Michel Raynaud
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| Michel Raynaud | |
|---|---|
| Name | Michel Raynaud |
| Birth date | 16 December 1938 |
| Birth place | Clermont-Ferrand, Puy-de-Dôme, France |
| Death date | 28 March 2018 |
| Death place | Paris, France |
| Nationality | French |
| Fields | Mathematics |
| Alma mater | École Normale Supérieure, University of Paris |
| Doctoral advisor | Alexandre Grothendieck |
Michel Raynaud was a French mathematician known for deep contributions to algebraic geometry, arithmetic geometry, and scheme theory. He worked on problems connected to the theories of Alexandre Grothendieck, Jean-Pierre Serre, Pierre Deligne, Grothendieck's scheme theory, and Éléments de géométrie algébrique. His research influenced developments related to the Mordell conjecture, Tate conjecture, Weil conjectures, and the arithmetic of algebraic curves.
Early life and education
Raynaud was born in Clermont-Ferrand in the department of Puy-de-Dôme and studied at the École Normale Supérieure where he encountered contemporaries associated with the mathematical schools of Bourbaki, Jean Dieudonné, and Alexander Grothendieck. He completed doctoral work under the supervision of Alexandre Grothendieck at the University of Paris while interacting with figures from IHÉS, Collège de France, and the CNRS community. His early formation involved engagement with the literature of Oscar Zariski, Jacob T. Schwartz, Jean-Pierre Serre, and seminars at the Séminaire Bourbaki.
Mathematical career and positions
Raynaud held positions at institutions including the University of Paris-Sud, the University of Grenoble, and the Collège de France circle via collaborations with researchers at Université Paris-Saclay, CNRS, and IHÉS. He supervised doctoral students and participated in international conferences organized by bodies such as the International Congress of Mathematicians, the European Mathematical Society, and the American Mathematical Society. He served on editorial boards for journals related to Annales scientifiques de l'École normale supérieure and interacted with mathematicians from Harvard University, Princeton University, Cambridge University, University of California, Berkeley, and École Polytechnique. Raynaud's career featured visiting appointments and collaborative work with researchers connected to Institute for Advanced Study, Max Planck Institute for Mathematics, and departments at Université de Lyon.
Major contributions and theorems
Raynaud produced results on degenerations of Jacobians, Néron models, and the structure of abelian varieties, engaging with concepts introduced by André Néron, John Tate, Armand Borel, and Hermann Weyl. He proved a pivotal case of the Abel–Jacobi map behavior in families and contributed to the understanding of the Tate–Shafarevich group for abelian varieties, building on the work of Birch and Swinnerton-Dyer and the framework of Grothendieck duality. Raynaud is noted for the "Raynaud criterion" on reduction of abelian varieties and for counterexamples to conjectures attributed to Alexander Grothendieck and Jean-Pierre Serre, influencing studies by Pierre Deligne and Nicholas Katz.
He resolved questions concerning the compactification of moduli spaces of curves, intersecting with research by David Mumford, Igor Shafarevich, David Gieseker, and Robert Coleman. Raynaud established results about formal schemes and rigid analytic spaces that related to the theories of John Tate and Vladimir Drinfeld, and his work on flat cohomology and group schemes extended the foundations laid by Michel Demazure and Alexander Grothendieck.
His proof of the Abhyankar conjecture in certain cases and contributions to the study of fundamental groups of algebraic varieties connected to the efforts of Shreeram Abhyankar, Alexander Grothendieck, Jean-Pierre Serre, and Grothendieck's Galois theory impacted subsequent progress by researchers at University of Chicago, Columbia University, and the Institute for Advanced Study. Raynaud also produced influential examples and counterexamples regarding Picard schemes and the behavior of line bundles, influencing subsequent work by Mumford, Grothendieck, and Serre.
Awards and honors
Raynaud received prizes and recognition from French and international bodies, including awards administered by institutions such as the Académie des Sciences and memberships in academies like the French Academy of Sciences and associations with the European Academy of Sciences. He was invited to speak at the International Congress of Mathematicians and received fellowships connected to research centers including IHÉS and the Institute for Advanced Study. His honors paralleled recognition received by contemporaries like Jean-Pierre Serre, Pierre Deligne, Alexander Grothendieck, and David Mumford.
Personal life and legacy
Raynaud's influence persists through students and collaborators at universities such as Université Paris-Sud, Université Paris-Saclay, University of Grenoble Alpes, and through citations in work by mathematicians at Harvard University, Princeton University, Cambridge University, and École Normale Supérieure. His legacy includes contributions to the pedagogy of algebraic geometry in seminars like the Séminaire Bourbaki and the propagation of ideas from Grothendieck and Weil. Memorials and obituaries appeared in venues associated with CNRS, Académie des Sciences, and departmental announcements at Université Paris-Sud.