Twistor D-Modules and the Decomposition Theorem

  • Takuro Mochizuki

    Kyoto University, Japan
  • Claude Sabbah

    Ecole polytechnique, Institut Polytechnique de Paris, Palaiseau, France

Abstract

The purpose of this Arbeitsgemeinschaft is to introduce the notion of twistor -modules and their main properties. The guiding principle leading this discussion is Simpson’s “meta-theorem”, which gives a heuristic for generalizing (mixed) Hodge-theoretic results into (mixed) twistor-theoretic results. The strength of the twistor approach is that it enables to enlarge the scope of Hodge theory not only to arbitrary semi-simple perverse sheaves, equivalently semi-simple regular holonomic -modules via the Riemann-Hilbert correspondence, but also to possibly semi-simple irregular holonomic -modules. An overarching goal for this session is Mochizuki’s proof of the decomposition theorem for semi-simple holonomic -modules on a smooth complex projective variety, first conjectured by Kashiwara in 1996.

Cite this article

Takuro Mochizuki, Claude Sabbah, Twistor D-Modules and the Decomposition Theorem. Oberwolfach Rep. 20 (2023), no. 2, pp. 927–964

DOI 10.4171/OWR/2023/17