Mathematics – Algebraic Geometry
Scientific paper
2011-07-28
Mathematics
Algebraic Geometry
This is my talk at the Arbeitstagung in Bonn, June 2011, dedicated to Zagier's 60th birthday
Scientific paper
The Hodge Galois group is the Tannakian Galois group of the category of real mixed Hodge structures. It has a subgroup, called the twistor Galois group, which is the Galois group of the category of mixed twistor structures, defined by C. Simpson. It is isomorphic to a semidirect product of C* and the unipotent radical of the Hodge Galois group. We define a natural action of the twistor Galois group by A-infinity autoequivalences of the derived category of complexes of sheaves with smooth cohomology on a compact smooth Kahler manifold X. The action of C* is provided by Simpson's action on irreducible local systems, and the action of the unipotent radical is given explicitly by the Hodge correlators for irreducible local systems on X. The Hodge correlators can be interpreted as correlators of cetrtain Feynman integrals. One should have a similar construction for the whole derived category of all holonomic D-modules.
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