Characteristic cycle and wild Lefschetz theorems

Abstract

By relying on a new approach to Lefschetz type questions based on Beilinson's singular support and Saito's characteristic cycle, we prove an instance of the wild Lefschetz theorem envisioned by Deligne. Our main tool are new finiteness results for the characteristic cycles of perverse sheaves.

v2: Hyperplane case written in a separate section from the higher codimension case. Wild Lefschetz restricted to finite coefficients due to an inaccuracy in [ES21]. See https://page.mi.fu-berlin.de/esnault/preprints/helene/138b_small_erratum.pdf for a correction. v3: Final version. To appear in J. für die Reine und Angew. Math