On the p-adic cohomology of the Lubin-Tate tower

We prove a finiteness result for the p-adic cohomology of the Lubin-Tate tower. For any n ≥ 1 and p-adic field F , this provides a canonical functor from admissible p-adic representations of GLn(F ) towards admissible p-adic representations of GalF ×D×, where GalF is the absolute Galois group of F , and D/F is the central division algebra of invariant 1/n. Moreover, we verify a local-global-compatibility statement for this correspondence, and compatibility with the patching construction of Caraiani-Emerton-Gee-GeraghtyPaskunas-Shin.