2018/07/03 by Bode, Andreas · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1807.01086
We study the behaviour of D-cap-modules on rigid analytic varieties under pushforward along a proper morphism. We prove a D-cap-module analogue of Kiehl's Proper Mapping Theorem, considering the derived sheaf-theoretic pushforward from DX-cap-modules to f_*DX-cap-modules for proper morphisms f: X→ Y. Under assumptions which can be naturally interpreted as a certain properness condition on the cotangent bundle, we show that any coadmissible DX-cap-module has coadmissible higher direct images. This implies among other things a purely geometric justification of the fact that the global sections functor in the rigid analytic Beilinson--Bernstein correspondence preserves coadmissibility, and we are able to extend this result to twisted D-cap-modules on analytified partial flag varieties.