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Vanishing theorems for the mod $p$ cohomology of some simple Shimura varieties

We show that the mod $p$ cohomology of a simple Shimura variety treated in Harris-Taylor's book vanishes outside a certain nontrivial range after localizing at any non-Eisenstein ideal of the Hecke algebra. In cases of low dimensions, we show the vanishing outside the middle degree.

preprint2020arXivOpen access
Teruhisa Koshikawa
math.RTmath.AGmath.NT
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Teruhisa Koshikawa

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