Related papers: On the $p$-adic theory of local models

We show that the v-sheaf local models of moduli spaces of $p$-adic shtukas are unibranch. In particular, this proves that the scheme-theoretic local models defined in our joint work with Ansch\"{u}tz and Richarz are always normal with…

We give a group theoretic definition of "local models" as sought after in the theory of Shimura varieties. These are projective schemes over the integers of a $p$-adic local field that are expected to model the singularities of integral…

We introduce the specialization map in Scholzes theory of diamonds. We consider v-sheaves that behave like formal schemes and call them kimberlites. We attach to them: a reduced special fiber, an analytic locus, a specialization map, a…

We study the Scholze test functions for bad reduction of simple Shimura varieties at a prime where the underlying local group is any inner form of a product of Weil restrictions of general linear groups. Using global methods, we prove that…

We use Scholze's framework of diamonds to gain new insights in correspondences between $p$-adic vector bundles and local systems. Such correspondences arise in the context of $p$-adic Simpson theory in the case of vanishing Higgs fields. In…

We extend the group theoretic construction of local models of Pappas and Zhu to the case of groups obtained by Weil restriction along a possibly wildly ramified extension. This completes the construction of local models for all reductive…

Using a mixed-characteristic incarnation of fusion, we prove an analog of Nekov\'a\v{r}-Scholl's plectic conjecture for local Shimura varieties. We apply this to obtain results on the plectic conjecture for (global) Shimura varieties after…

We prove the test function conjecture of Kottwitz and the first named author for local models of Shimura varieties with parahoric level structure attached to Weil-restricted groups, as defined by B. Levin. Our result covers the (modified)…

We show that the moduli spaces of Scholze's $p$-adic shtukas with framing satisfy a $p$-adic rigid analytic version of Borel's extension theorem. In particular, this holds for local Shimura varieties, for all local Shimura data…

Kottwitz's conjecture describes the contribution of a supercuspidal represention to the cohomology of a local Shimura variety in terms of the local Langlands correspondence. A natural extension of this conjecture concerns Scholze's more…

We construct a K-theory version of Bhatt-Morrow-Scholze's Breuil-Kisin cohomology theory for $\sO_K$-linear idempotent-complete, small smooth proper stable infinity-categories, where $K$ is a discretely valued extension of $\Q_p$ with…

We give a construction of "integral local Shimura varieties" which are formal schemes that generalize the well-known integral models of the Drinfeld $p$-adic upper half spaces. The construction applies to all classical groups, at least for…

We compute the connected components of arbitrary parahoric level affine Deligne-Lusztig varieties and local Shimura varieties, thus resolving a folklore conjecture in full generality (even for non-quasisplit groups). We achieve this by…

We prove a number of results on the \'etale cohomology of rigid analytic varieties over $p$-adic non-archimedean local fields. Among other things, we establish bounds for Frobenius eigenvalues, show a strong version of Grothendieck's local…

For a proper, flat, generically smooth scheme $X$ over a complete DVR with finite residue field of characteristic $p$, we define a specialization morphism from the rigid cohomology of the geometric special fibre to $D_{crys}$ of the…

This is a survey article that advertizes the idea that there should exist a theory of p-adic local analogues of Shimura varieties. Prime examples are the towers of rigid-analytic spaces defined by Rapoport-Zink spaces, and we also review…

We consider the local model of a Shimura variety of PEL type, with the unitary similitudes corresponding to a ramified quadratic extension of $\mathbb{Q}_p$ as defining group. We examine the cases where the level structure at $p$ is given…

This paper is a continuation of our paper math.AG/0006222. We study the reduction of certain PEL Shimura varieties with parahoric level structure at primes p at which the group that defines the Shimura variety ramifies. We describe "good"…

We elaborate the theory of the stable Bernstein center of a $p$-adic group $G$, and apply it to state a general conjecture on test functions for Shimura varieties due to the author and R. Kottwitz. This conjecture provides a framework by…

We prove the uniqueness of the Ginzburg-Rallis models over $p$-adic local fields of characteristic zero, which completes the local uniqueness problem for the Ginzburg-Rallis models starting from the work of C.-F. Nien in \cite{MR2709083}…