Degeneration of the noncommutative Hodge-to-de Rham spectral sequences (GPS)
Student No.:50
Time:Tue 9:00-10:30, 2017-6-27
Instructor:Jingyu Zhao  [Institute of Advanced Study]
Place:Conference room 4, Floor 2, Jin Chun Yuan West Building
Starting Date:2017-6-27
Ending Date:2017-6-27


For a compact Kahler manifold, the Hodge-to-de Rham spectral sequence degenerates at E^1 page. This can be proved using Hodge theory which is highly transcendental. In 1982, Deligne and Illusie gave a purely algebraic proof of the degeneration of the Hodge-to-de Rham spectral sequences using reduction to characteristic p methods. For a DG category, there is a noncommutative Hodge-to-de Rham spectral sequence which relates the Hochschild homology and periodic cyclic homology of A. It is conjectured by Kontsevich and Soibelman and proved by Kaledin in 2016 that the noncommutative Hodge-to-de Rham spectral sequences degenerates for smooth and proper DG categories. In this lecture, we give an outline of the proof of degeneration following Kaledin’s work. The key step is to prove a non-commutative analogue of the Cartier isomorphism in the work of Deligne and Illusie.


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