Urs Hartl

The Newton stratification on deformations of local G-shtukas

Abstract Bounded local G-shtukas are function field analogs for p-divisible groups with extra structure. We describe their deformations and moduli spaces. The latter are analogous to Rapoport–Zink spaces for p-divisible groups. The underlying schemes of these moduli spaces are affine Deligne–Lusztig varieties. For basic Newton polygons the closed Newton stratum in the universal deformation of a local G-shtuka is isomorphic to the completion of a corresponding affine Deligne–Lusztig variety in that point. This yields bounds on the dimension and proves equidimensionality of the basic affine Deligne–Lusztig varieties.

Vector bundles with a Frobenius structure on the punctured unit disc

Let

A Dictionary between Fontaine-Theory and its Analogue in Equal Characteristic

\mathbb{C}

Foliations in deformation spaces of local G-shtukas

be a complete non-archimedean-valued algebraically closed field of characteristic p > 0 and consider the punctured unit disc

Pure Anderson motives and abelian τ-sheaves

\dot{D} \subset \mathbb{C}

Uniformizing the Stacks of Abelian Sheaves

. Let q be a power of p and consider the arithmetic Frobenius automorphism

Local P-shtukas and their relation to global G-shtukas

\sigma_{\dot{D}}: x \mapsto x^{q^{-1}}

On period spaces for p-divisible groups

. A

Uniformizable families of

\sigma

t

- bundle is a vector bundle