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Non-commutative Cartier isomorphism

SPEAKER: Dmitry Vaintrob

TITLE: Non-commutative Cartier isomorphism.

ABSTRACT: The classical Hodge isomorphism, which splits the de Rham cohomology of a complex projective (more generally, Kahler) manifold X into Hodge constituents coming from cohomology of complex differential forms, has a very satisfying analogue in characteristic-p algebraic geometry, called the Cartier isomorphism. It turns out that the Cartier isomorphism can be stated and proved using only the structure of the category coh(X) of coherent sheaves on X, and the appropriate statement for general (smooth) categories, called the “noncommutative Cartier isomorphism”, was proved recently by Dmitry Kaledin using ideas from topology. I will present (a modified version of) Kaledin’s proof.