In this note, we introduce and study the Cartier--Witt stack $\mathrm {WCart} _X $ attached to
a $ p $-adic formal scheme $ X $ as well as some variants. In particular, we reinterpret the …

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 …

We study Hodge--Tate crystals on the absolute (log-) prismatic site of $\mathcal {O} _K $,
where $\mathcal {O} _K $ is a mixed characteristic complete discrete valuation ring with …

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 …

Let $\mathcal {O} _K $ be a mixed characteristic complete discrete valuation ring with perfect
residue field. We classify de Rham crystals over the (log-) prismatic site of $\mathcal {O} _K …

Let $ p $ be a prime, $ W $ the ring of Witt vectors of a perfect field $ k $ of characteristic $ p
$ and $\zeta $ a primitive $ p $ th root of unity. We introduce a new notion of calculus over …

Let $\calO_K $ be a complete discrete valuation ring of mixed characteristic $(0, p) $ with a
perfect residue field. In this paper, for a semi-stable $ p $-adic formal scheme $\frakX $ over …

We study de Rham prismatic crystals on. We show that a de Rham crystal is controlled by a
sequence of matrices {A m, 1} m≥ 0 with A 0, 1 “nilpotent”. Using this, we prove that the …