Abstract: In the two talks, I will introduce a main result on the upper bound of each Betti number of an étale sheaf on a positive characteristic variety and explain several applications. These results are joint with Jean-Baptiste Teyssier.
In the first talk, I will focus on the statement of the main result, the sketch of the proof, and an application in a generalization of Deligne’s finiteness theorem for l-adic sheaves with bounded ramification.
In the second talk, I will sketch applications in a finiteness result for irreducible components of singular supports, and in a Lefschetz type theorem for monodromy groups.
