Continuing a lineage of pioneering works initiated by Weil in 1958 and developed mainly by
Narashiman–Seshadri, Donaldson, Hitchin and Corlette, Simpson made a significant …

The p-adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing
all p-adic representations of the fundamental group of a proper smooth variety over a p-adic …

For curves over a p-adic field we construct an equivalence between the category of Higgs-
bundles and that of “generalised representation” of the etale fundamental group. The …

VI. 1.1. The aim of this chapter is to consolidate the topogical foundation necessary for
Faltings' approach in p-adic Hodge theory [24, 26, 27]. Its genesis has been motivated by …

A P-adic Simpson Correspondence II: Small Representations Page 1 Pure and Applied
Mathematics Quarterly Volume 7, Number 4 (Special Issue: In memory of Eckart Viehweg) …

1.1. The last decade has been a time of tremendous activity in p-adic Hodge Theory. We do
not intend to give a complete account of these new developments here, but let us at least …

Given a proper smooth $ p $-adic variety, we show a comparison theorem for the $ p $-adic
Simpson correspondence constructed by Faltings and Riemann-Hilbert correspondence …

We develop and study three instances for descent in p-adic Hodge theory. In the first part,
we establish a cohomological descent for Faltings'p-adic Hodge theory. Faltings' approach …

(0.0) In the theory of p-adic representation of the Galois group of a p-adic field, there has
been great interest in showing the existence of Hodge-Tate structures for certain" nice" p …

This thesis aims to expose the amazing sequence of ideas, concerning p-adic
representations coming from geometry, that form the heart of what was called Hodge-Tate …