Related papers: Local models in the ramified case. II. Splitting m…

In this paper, we reformulate conjectural formulas for the arithmetic intersection numbers of special cycles on unitary Shimura varieties with minuscule parahoric level structure in terms of weighted counting of lattices containing special…

We prove a conjecture of Pappas and Rapoport for all Shimura varieties of abelian type with parahoric level structure when $p>3$ by showing that the Kisin-Pappas-Zhou integral models of Shimura varieties of abelian type are canonical. In…

We consider Hilbert modular varieties in characteristic p with Iwahori level at p and construct a geometric Jacquet-Langlands relation showing that the irreducible components are isomorphic to products of projective bundles over…

We introduce the ramified partition algebra, which is a physically motivated and natural generalization of the partition algebra. We investigate its representation theory and demonstrate quasi--heredity under certain conditions. Under these…

In this paper, we give lower bounds for the homology of the fibers of a map to a manifold. Using new sheaf theoretic methods, we show that these lower bounds persist over whole open sets of the manifold, and that they are stable under…

Let $A$ be a regular 2-dimensional local ring of characteristic $p>0$, and let $L/K$ be a cyclic extension of degree $p$ of its field of fractions such that the corresponding branch divisor is normal crossing. For each $\gp\in\Spec A$ of…

Let p be an odd prime. Let G be a p-local finite group over the extraspecial p-group p_+^{1+2}. In this paper we study the cohomology and the stable splitting of their p-complete classifying space BG.

Let $F$ be a totally real field in which $p$ is unramified. We study the Goren-Oort stratification of the special fibers of quaternionic Shimura varieties over a place above $p$. We show that each stratum is a $(\mathbb{P}^1)^N$-bundle over…

We prove that Shimura varieties admit integral canonical models for sufficiently large primes. In the case of abelian-type Shimura varieties, this recovers work of Kisin-Kottwitz for sufficiently large primes. We also prove the existence of…

We study the supersingular locus of a reduction at an inert prime of the Shimura variety attached to $\mathrm{GU}(2,n-2)$. More concretely, we decompose the supersingular locus into a disjoint union of iterated fibrations over (classical)…

We propose topological Hochschild homology as a tool for measuring ramification of maps of structured ring spectra. We determine second order topological Hochschild homology of the $p$-local integers. For the tamely ramified extension of…

We study the reduction of certain integral models of Shimura varieties of PEL type with Iwahori level structure. On these spaces we have the Kottwitz-Rapoport and the $p$-rank stratification. We show that the $p$-rank is constant on a KR…

For the ring R of integers of a ramified extension of the field of p-adic numbers and a cyclic group G of prime order p we study the extensions of the additive groups of R-representations modules of G by the group G.

We introduce moduli spaces of abelian varieties which are arithmetic models of Shimura varieties attached to unitary groups of signature (n-1, 1). We define arithmetic cycles on these models and study their intersection behaviour. In…

Let $F$ be a local field over $\mathbf{Q}_p$ or $\mathbf{F}_p((t))$, and let $D$ be a central simple division algebra over $F$ of degree $d$. In the $p$-adic case, we assume $p>de+1$ where $e$ is the ramification degree over $\mathbf{Q}_p$;…

We study the ramified Prym map $\mathcal P_{g,r} \longrightarrow \mathcal A_{g-1+\frac r2}^{\delta}$ which assigns to a ramified double cover of a smooth irreducible curve of genus $g$ ramified in $r$ points the Prym variety of the…

If $S$ is a scheme of characteristic $p$, we define an $F$-zip over $S$ to be a vector bundle with two filtrations plus a collection of semi-linear isomorphisms between the graded pieces of the filtrations. For every smooth proper morphism…

Under simplifying hypotheses we prove a relation between the l-adic cohomology of the basic stratum of a Shimura variety of PEL-type modulo a prime of good reduction of the reflex field and the cohomology of the complex Shimura variety. In…

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…

In this article we use a Prym construction to study low dimensional abelian varieties with an action of the quaternion group. In special cases we describe the Shimura variety parameterizing such abelian varieties, as well as a map to this…