A mod-p Lubin-Tate tower and applications to chromatic homotopy theory
报告人：Lucas Mann ( University of Münster )
时间：2025-12-1 15:00-16:00
地点：镜春园77201
Abstract: In 2024 Barthel--Schlank--Stapleton--Weinstein proved the rational version of the chromatic splitting conjecture, a deep conjecture on homotopy groups of spheres that previously seemed out of reach. Their method crucially uses p-adic geometry, specifically the isomorphism of the Drinfeld and Lubin--Tate towers. In a recent joint project initiated at an AIM workshop, we attack the integral (i.e. mod p) version of the splitting conjecture by similar methods. We construct a mod p version of the Lubin--Tate tower and Drinfeld tower and use them to relate the splitting conjecture to the computation of a certain p-adic cohomology on Drinfeld's upper half space. We then use the recent 6-functor formalism of Anschütz--Le-Bras--Mann to compute this cohomology. Our computation in particular predicts the existence of an unexpected error term in the splitting conjecture for small primes.
