On the generic part of the cohomology of non-compact PEL-type A Shimura varieties

In this thesis, we use the new methods of Koshikawa to prove that the generic l-adic cohomology of non-compact type A Shimura varieties vanishes below middle degree, when localized at a maximal ideal of the Hecke algebra. This generalizes previously established vanishing results of Caraiani-Scholze.Open Acces