Related papers: Log Prismatic Dieudonn\'{e} theory and its applica…

Let $\mathcal{O}_{K}$ be a complete discrete valuation ring of mixed characteristic with perfect residue field, endowed with its canonical log-structure. We prove that log $p$-divisible groups over $\mathcal{O}_{K}$ correspond to…

We construct projective toroidal compactifications for integral models of Shimura varieties of Hodge type. We also construct integral models of the minimal (Satake-Baily-Borel) compactification. Our results essentially reduce the problem to…

We study families of analytic $p$-divisible groups over adic spaces $S$ defined over $\mathbb{Q}_p$. We prove an equivalence between such families and Hodge-Tate triples, generalizing a theorem of Fargues. For a perfectoid space $S$, we…

In this paper, we construct good toroidal and minimal compactifications in the sense of Lan-Stroh for integral models of abelian-type Shimura varieties. We start with finding suitable types of cusp labels and cone decompositions which are…

We determine the irreducible components of Igusa varieties for Shimura varieties of Hodge type under a mild condition and use that to compute the irreducible components of central leaves. In particular, we show that a strong version of the…

We study a cohomology theory for rigid-analytic varieties over $\mathbb{C}_p$, without properness or smoothness assumptions, taking values in filtered quasi-coherent complexes over the Fargues-Fontaine curve, which compares to other…

We construct log-motivic cohomology groups for semistable varieties and study the $p$-adic deformation theory of log-motivic cohomology classes. Our main result is the deformational part of a $p$-adic variational Hodge conjecture for…

In this paper, we apply stack theoretic ideas to the classification problem in Dieudonn\'e theory. First, we use crystalline cohomology of classifying stacks to directly reconstruct the classical Dieudonn\'e module of a finite, $p$-power…

We construct canonical extensions of $p$-adic shtukas on integral models of toroidal compactifications of abelian-type Shimura varieties with quasi-parahoric levels at any prime number $p$. More precisely, we define the notion of a log…

We give a new proof of Ohta's Lambda-adic Eichler-Shimura isomorphism using p-adic Hodge theory and the results of Bloch-Kato and Hyodo on p-adic etale cohomology.

For any Shimura variety of Hodge type with hyperspecial level at a prime $p$ and automorphic lisse sheaf on it, we prove a formula, conjectured by Kottwitz \cite{Kottwitz90}, for the Lefschetz numbers of Frobenius-twisted Hecke…

Let $(\mathsf{G},\mathsf{X})$ be a Shimura datum of Hodge type. Let $p$ be an odd prime such that $\mathsf{G}_{\mathbb{Q}_p}$ splits after a tamely ramified extension and $p\nmid |\pi_1(\mathsf{G}^{\rm der})|$. Under some mild additional…

We show Eicher-Shimura relations for some Shimura varieties of Hodge type, proving a conjecture of Blasius and Rogawski in this case. We show this using a parabolic reduction strategy on the Hecke action on irreducible components of affine…

In this paper, we generalize a conjecture due to Darmon and Logan in an adelic setting. We study the relation between our construction and Kudla's works on cycles on orthogonal Shimura varieties. This relation allows us to conjecture a…

We prove the isogeny property for special fibres of integral canonical models of compact Shimura varieties of $A_n$, $B_n$, $C_n$, and $D_n^{\dbR}$ type. The approach used also shows that many crystalline cycles on abelian varieties over…

We reinterpret and generalize the construction of local Shimura varieties and their non-minuscule analogs by viewing them as moduli spaces of admissible pairs. Our main application is a bi-analytic Ax-Lindemann theorem comparing, in the…

Classical Hodge theory endows the square integrable cohomology of a Shimura variety X with values in a locally homogeneous polarized variation of Hodge structure E with a natural Hodge decomposition. The theory of Morihiko Saito does the…

In this paper, we establish an innovative framework in logarithmic Hodge theory for toroidal varieties, introducing weighted toroidal structures and developing a systematic obstruction theory for Hodge classes. Building upon recent advances…

We give a simple proof that Kottwitz's PEL type integral models of Shimura varieties admit closed embeddings into Siegel integral models. We also show that Rapoport's and Kottwitz's integral models agree with Kisin's integral models for…

We prove an analogue for Hodge modules of Pink's theorem on the degeneration of l-adic sheaves (Math. Ann. 292). Let j be the open immersion of a Shimura variety M into its Baily-Borel compactification. Its boundary has a natural…