A perverse proof of the Weil conjecture

Speaker：Dingxin Zhang (SIMIS)

Time：2026-4-9 14:00

Location：Conference Room S306 at Experiment Building at Haiyun Campus

Abstract:

I will present a streamlined proof of the Riemann hypothesis for varieties over finite fields. The talk consists of two parts. First, I explain how Deligne's interpretation of Rankin's method enables Katz to reduce the Riemann hypothesis for smooth projective hypersurfaces to elementary examples where one can verify the relevant estimates by hand. Second, I introduce the defining properties of perverse sheaves and explain how Artin vanishing yields a degeneration lemma. This lemma provides a mechanism to complete the proof which avoids the technical apparatus of standard cohomological methods, such as monodromy computations and Lefschetz pencils as in Deligne's original proof, or alterations and the Steenbrink–Rapoport–Zink spectral sequence as in Tony Scholl's proof.