Non-Archimedean Analytic Singular Homology Based On Cosimplicial   Perfectoid Spaces and Integration along Cycles
  We introduce singular homology for non-Archimedean analytic spaces using a cosimplicial perfectoid space as a Galois representation. We define an integration along a cycle, which gives a pairing with the singular homology and the space of differential forms. 
Tomoki Mihara
math.NT math.AG