We propose a new moduli theoretic approach to the $ p $-adic Simpson correspondence for
a smooth proper rigid space $ X $ with coefficients in any rigid analytic group $ G $, in terms …

Let X be a smooth p-adic formal scheme over OK with adic generic fibre X. We obtain a
global equivalence between the category Vect.. X/¡; xO¡ Œ 1 p/of rational Hodge–Tate …

For any smooth proper rigid analytic space $ X $ over a complete algebraically closed
extension of $\mathbb Q_p $, we construct a $ p $-adic Simpson correspondence: an …

Let 𝑋 be a quasi-compact quasi-separated 𝑝-adic formal scheme that is smooth either over
a perfectoid Z p-algebra or over some ring of integers of a 𝑝-adic field. We construct a fully …

We describe the category of continuous semilinear representations and their cohomology for
the Galois group of a $ p $-adic field $ K $ with coefficients in a completed algebraic closure …

For any rigid space over a perfectoid extension of $\mathbb Q_p $ that admits a liftable
smooth formal model, we construct an isomorphism between the moduli stacks of Hitchin …

For any smooth proper rigid space $ X $ over a complete algebraically closed extension $ K
$ of $\mathbb {Q} _p $ we give a geometrisation of the $ p $-adic Simpson correspondence …

We explore generalizations of the $ p $-adic Simpson correspondence on smooth proper
rigid spaces to principal bundles under rigid group varieties $ G $. For commutative $ G …

arXiv:2205.02016v2 [math.NT] 31 Aug 2022 Page 1 arXiv:2205.02016v2 [math.NT] 31 Aug 2022
GEOMETRIC SEN THEORY OVER RIGID ANALYTIC SPACES JUAN ESTEBAN RODRÍGUEZ …

Let $ X $ be a quasi-compact quasi-separated $ p $-adic formal scheme that is smooth
either over a perfectoid $\mathbb {Z} _p $-algebra or over some ring of integers of a $ p …