Periodic Reporting for period 4 - HiCoShiVa (Higher coherent coholomogy of Shimura varieties)
Reporting period: 2023-08-01 to 2024-07-31
The applications are to the construction of automorphic Galois representations, the modularity of irregular motives and new cases of the Hasse-Weil conjecture, and the construction of p-adic L-functions.
The main outcomes are the proof of the potential modularity of abelian surfaces (with Boxer, Calegari, Gee) (>300 pages manuscript published in Publ. Math. IHES) and Higher Coleman theory (with Boxer) (175 pages preprint).