Olivier Fouquet
Research
I am currently a post-doc at Osaka University and visiting UCLA. I did my Ph.D. as a member of the Number Theory team at the Institut de Mathématiques de Jussieu.
My research interests are :
- p-adic variation of motives and deformation theory.
- arithmetic geometry, especially arithmetic properties of Shimura and modular varieties.
- Iwasawa theory
- Euler/Kolyvagin systems
My Ph.D. work was on the construction and study of integral Galois representations arising from tower of Shimura curves. More precisely, I constructed cohomology classes satisfying compatibility relations similar to those of an Euler/Kolyvagin system. I worked under the supervision of Jan Nekovář. I used this class to prove various results in Iwasawa theory of automorphic forms. I am also interested in control theorem for Selmer groups and complexes in p-adic families of automorphic forms and their links to the Equivariant Tamagawa Number Conjecture.
My Ph.D. defence took place on Monday, December 17, 2007 at 14h30.
Publications and preprints
Tour de courbes de Shimura, systèmes de Kolyvagin et théorie d'Iwasawa des formes modulaires ordinaires, thèse de doctorat de l'Université Paris VI (2007) - pdf
Systèmes d'Euler pour les tours de courbes de Shimura, to appear in Actes du Colloque Cohomologie l-adique et Corps de Nombres (2007) - pdf
Dihedral Iwasawa theory of quaternionic automorphic forms, submited - pdf
Euler systems in the Iwasawa theory of modular forms, to appear in RIMS Kokyuroku Bessatsu Series - pdf
Control theorems for Selmer groups of nearly ordinary deformations, with T.Ochiai - pdf
Teaching
Last
semester, I co-organized Mathematic 290b at UCLA with Haruzo Hida and Chandrashekar Khare. Notes from this course can be found at the linked page. Before that, I taught various LM 220 courses at Université Pierre et Marie Curie.