Related papers: On Shimura varieties for unitary groups

Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex special linear two dimensional representations of the…

We establish new upper bounds about symmetric bilinear complexity in any extension of finite fields. Note that these bounds are not asymptotical but uniform. Moreover we give examples of Shimura curves that do not descend over their field…

This survey article is intended as an introduction to the recent categorical classification theorems of the three authors, restricting to the special case of the category of modules for a finite group.

This is the second paper in a series on enumerative invariants counting self-dual objects in self-dual categories, and is a sequal to (arXiv:2302.00038). Ordinary enumerative invariants in abelian categories can be seen as invariants for…

Shimura reciprocity law allows us to verify that a modular function is a class invariant. Here we present a new method based on Shimura reciprocity that allows us not only to verify but to find new class invariants from a modular function…

We present a novel axiomatic framework for establishing horizontal norm relations in Euler systems that are built from pushforwards of classes in the motivic cohomology of Shimura varieties. This framework is uniformly applicable to the…

Let $A$ be a Nakayama algebra. We give a description of the singularity category of $A$ inside its stable module category. We prove that there is a duality between the singularity category of $A$ and the singularity category of its opposite…

In this paper we construct Shimura subvarieties of dimension bigger than one of the moduli space of polarised abelian varieties of a given dimension, which are generically contained in the Pym loci of (ramified) double covers. The idea is…

In this article we analyze the structure of $2$-categories of symmetric projective bimodules over a finite dimensional algebra with respect to the action of a finite abelian group. We determine under which condition the resulting…

Let $Y$ be a subvariety contained in a smooth Mumford compactification of an orthogonal Shimura variety $M \subset A_g$, where $A_g$ is the moduli space of principally polarized abelian varieties of dimension $g$ with some level structure,…

Consider a PEL-Shimura variety associated to a unitary group that splits over an unramified extension of Q_p. Rapoport and Zink have defined a model of the Shimura variety over the ring of integers of the completion of the reflex field at a…

In this paper, we provide a classification of certain points on Hilbert modular varieties over finite fields under a mild assumption on Newton polygon. Furthermore, we use this characterization to prove estimates for the size of isogeny…

In this article we give explicit equations for two Shimura families of genus 4 curves whose Jacobians are abelian fourfolds of Mumford type. These are the first explicit examples of abelian varieties over $\mathbb{Q}$ with endomorphism…

In this paper we study the Oort conjecture on Shimura subvarieties contained generically in the Torelli locus in the Siegel modular variety $\mathcal{A}_g$. Using the poly-stability of Higgs bundles on curves and the slope inequality of…

In this note, we consider special algebraic cycles on the Shimura variety S associated to a quadratic space V over a totally real field F, |F:\Q|=d, of signature ((m,2)^{d_+},(m+2,0)^{d-d_+}), 1\le d_+<d. For each n, 1\le n\le m, there are…

Recent developments on the uniformity of the number of rational points on curves and subvarieties in a moving abelian variety rely on the geometric concept of the degeneracy locus. The first-named author investigated the degeneracy locus in…

We study a Shimura variety attached to a unitary similitude group of a skew-Hermitian form over a totally indefinite quaternion algebra over a totally real number field. We give a necessary and sufficient condition for the existence of…

This is the third of a series of papers relating intersections of special cycles on the integral model of a Shimura surface to Fourier coefficients of Hilbert modular forms. More precisely, we embed the Shimura curve over Q associated to a…

To every abelian subvariety of a principally polarized abelian variety $(A, \mathcal{L})$ we canonically associate a numerical class in the N\'eron-Severi group of $A$. We prove that these classes are characterized by their intersection…

In this paper we use A-infinity modules to study the derived category of a finite dimensional algebra over an algebraically closed field. We study varieties parameterising A-infinity modules. These varieties carry an action of an algebraic…