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The ordinary part of higher coherent cohomology of Hilbert modular varieties

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The ordinary part of higher coherent cohomology of Hilbert modular varieties
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9
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I will introduce the ordinary part (in the sense of Hida) of the higher coherent cohomology of Hilbert modular varieties and explain what we know about it: vanishing results and Hida style control theorems. This is joint work in progress with Vincent Pilloni.