分野別セミナー

A p-adic analogue of Simpson correspondence between Higgs bundles
and representations of fundamental groups was given by G. Faltings
around ten years ago. His theory, however, depends on the choice of
a certain infinitesimal deformation of a variety, which may not exist in
general.
This problem can be resolved by working with a kind of crystals,
which I call "Higgs crystals", instead of bundles. With this point of view,
one can also naturally construct a "Higgs analogue"
of the p-adic period ring Acrys, and study the Galois cohomology
of the representation associated to a Higgs crystal.
I will first give an introduction of the work of Faltings,
and then talk on the results above.