Morihiko Saitō

Morihiko Saitō ( Japanese 斎藤盛彦 , Saitō Morihiko ; * 1961 ) is a Japanese mathematician who deals with algebraic analysis (theory of D modules based on algebraic varieties ) and algebraic geometry .

In 1988/1990 he introduced the theory of the mixed Hodge modules ( Mixed Hodge Modules ), based on the theory of D modules in algebraic analysis, the theory of perverse sheaves and the theory of the variation of Hodge structures and mixed Hodge structures (introduced by Pierre Deligne ) in Algebraic Geometry. This led, among other things, to an expansion of the fundamental theorems of Beilinson , Bernstein , Deligne , Ofer Gabber about perverse sheaves in positive characteristics to characteristic 0. The theory of the Hodge D modules formed the starting point for the theory of the Twistor D modules of Claude Sabbah and Takurō Mochizuki , which led to a further generalization of the theorems of Beilinson-Bernstein-Deligne-Gabber by Mochizuki.

He deals with the application of the theory of mixed Hodge structures and modules in algebraic geometry, for example the theory of singularities .

He was invited speaker at the 1990 International Congress of Mathematicians in Kyoto ( Mixed Hodge Modules and Applications ). In 1991 he received the Spring Prize of the Japanese Mathematical Society .

Fonts

Hodge structure via filtered D-Modules , Astérisque 130, 1985, 342-351
Modules de Hodge polarisables, Pubi. RIMS, Kyoto Univ. 24 (1988) 849-995
Mixed Hodge modules , Pubi. RIMS, Kyoto Univ. 26 (1990) 221-333
Decomposition theorem for proper Kähler morphisms , Tohoku Math. J. 42, 1990, pp. 127-148
with Nero Budur, Nero, Mircea Mustaţǎ Bernstein-Sato polynomials of arbitrary varieties , Compositio Mathematica 142, 2006, pp. 779–797
Introduction to mixed Hodge modules , in: Actes du Colloque de Théorie de Hodge (Luminy, 1987), Astérisque No. 179-180, 1989, pp. 145-162