相关论文: Kodaira-Spencer isomorphisms and degeneracy maps o…

We study minimal and toroidal compactifications of $p$-integral models of Hilbert modular varieties. We review the theory in the setting of Iwahori level at primes over $p$, and extend it to certain finer level structures. We also prove…

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…

The new compactification of moduli scheme of Gieseker-stable vector bundles with the given Hilbert polynomial on a smooth projective polarized surface (S;H), over the field k = \bar k of zero characteristic, is constructed in previous…

The goal of this paper is to explicitly compute the Kodaira-Spencer maps over Hilbert-Siegel modular varieties and twisted Hilbert modular varieties and their effects on the metrics of the Hodge bundle. Our result is a generalization of the…

We study integral models of some Shimura varieties with bad reduction at a prime $p$, namely the Siegel modular variety and Shimura varieties associated with some unitary groups. We focus on the case where the level structure at $p$ is…

We study birational maps among 1) the moduli space of semistable torsion sheaves of Hilbert polynomial $4m+2$ on a smooth quadric surface, 2) the moduli space of semistable torsion sheaves of Hilbert polynomial $m^{2}+3m+2$ on…

We give a new construction of $p$-adic overconvergent Hilbert modular forms by using Scholze's perfectoid Shimura varieties at infinite level and the Hodge--Tate period map. The definition is analytic, closely resembling that of complex…

We study the \'etale cohomology of Hilbert modular varieties, building on the methods introduced for unitary Shimura varieties in [CS17, CS19]. We obtain the analogous vanishing theorem: in the "generic" case, the cohomology with torsion…

We define the isomonodromic deformation of a Higgs bundle over a compact Riemann surface via the Hitchin-Simpson correspondence and the isomonodromic deformation of a local system. This deformation defines a real analytic section of the…

Let $A$ be an abelian scheme over a smooth affine complex variety $S$, $\varOmega_A$ the $\sO_S$-module of $1$-forms of the first kind on $A$, $\sD_S\varOmega_A$ the $\sD_S$-module spanned by $\varOmega_A$ in the first algebraic De Rham…

Let $G$ be a split connected reductive group over a finite field of characteristic $p > 2$ such that $G_\text{der}$ is absolutely almost simple. We give a geometric construction of perverse $\mathbb{F}_p$-sheaves on the Iwahori affine flag…

Let $X$ be a compact connected Riemann surface of genus $g$, with $g\geq 2$, and ${\cal M}_{\xi}$ a smooth moduli space of fixed determinant semistable vector bundles of rank $n$, with $n\geq 2$, over $X$. Take a smooth anticanonical…

We continue our study of integral points on moduli schemes by combining the method of Faltings (Arakelov, Parsin, Szpiro) with modularity results and Masser-W\"ustholz isogeny estimates. In this work we explicitly bound the height and the…

Let p be a prime number, and F a nonarchimedean local field of residual characteristic p. We explore the interaction between the pro-p-Iwahori-Hecke algebras of the group GL_n(F) and its derived subgroup SL_n(F). Using the interplay between…

We establish a connection between certain unique models, or equivalently unique functionals, for representations of p-adic groups and linear characters of their corresponding Hecke algebras. This allows us to give a uniform evaluation of…

Let \rho be a modulo p representation of the absolute Galois group of a totally real number field. Under the assumptions that \rho has large image and admits a low weight crystalline modular deformation we show that any low weight…

We study $p$-adic properties of the coherent cohomology of some automorphic sheaves on the Hilbert modular variety $X$ for a totally real field $F$ in the case where the prime $p$ is totally split in $F$. More precisely, we develop higher…

We describe explicitly the possible degenerations of a class of double Kodaira fibrations in the moduli space of stable surfaces. Using deformation theory we also show that under some assumptions we get a connected component of the moduli…

We construct the first examples of good type III degenerations of hyperk\"ahler varieties in dimension greater than 2. These are presented as moduli of 0-dimensional subschemes on expansions of a degeneration of K3 surfaces. We prove…

The Gieseker-Uhlenbeck morphism maps the Gieseker moduli space of stable rank-2 sheaves on a smooth projective surface to the Uhlenbeck compactification, and is a generalization of the Hilbert-Chow morphism for Hilbert schemes of points.…