Number Theory Web Seminar: Ana Caraiani (Imperial College London)

On the cohomology of Shimura varieties with torsion coefficients

Shimura varieties are certain highly symmetric algebraic varieties that generalise modular curves and that play an important role in the Langlands program. In this talk, I will survey recent vanishing conjectures and results about the cohomology of Shimura varieties with torsion coefficients, under both local and global representation-theoretic conditions. I will illustrate the geometric ingredients needed to establish these results using the toy model of the modular curve. I will also mention several applications, including to (potential) modularity over CM fields.

For further information about the seminar, please visit this webpage.

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