Arithmetic Geometry

I will discuss compatibility of the canonical $G$-valued $l$-adic local systems on Shimura varieties of non-abelian type $G$. In previous work with Klevdal, we settled this for the projections of the local systems to the adjoint group of $G$, and...

I will discuss new structural properties of the de Rham cohomology of smooth schemes over the ring of Witt vectors. The main technical input is the $F$-gauge structure on crystalline cohomology. First, I will explain the slope obstruction to the...

The singularities of integral models of Shimura varieties are encoded in their local models, schemes over the $p$-adic integers whose special fibers are unions of affine Schubert cells. A fundamental question is whether these local models are Cohen...