PT Unknown
AU Sheth, M
TI Locally analytic representations in the moduli spaces of Lubin-Tate
PD 02
PY 2018
LA en
AB Let K be a finite extension of Q_p with ring of integers o, and let H_0 be a formal o-module of finite height over a separable closure of the residue class field of K. The Lubin-Tate moduli space X_m classifies deformations of H_0 equipped with level-m-structure. In this thesis, we study a particular type of p-adic representations originating from the action of Aut(H_0) on certain equivariant vector bundles on the generic fibre of X_m . We show that, for arbitrary level m, the Fréchet space of the global sections of these vector bundles is dual to a locally K-analytic representation of Aut(H_0) generalizing previous results of J. Kohlhaase in the case K = Q_p and
m = 0. To get a better understanding of these representations, we compute their locally finite vectors. Essentially, all locally finite vectors arise from the global sections over the projective space via pullback along the Gross-Hopkins period map.
ER