Related papers: Shimura Varieties and Moduli
In [A. Aguglia, A. Cossidente, G. Korchmaros, "On quasi-Hermitian varieties", J. Comb. Des. 20 (2012), 433-447] new quasi-Hermitian varieties ${\mathcal M}_{\alpha,\beta}$ in $\mathrm{PG}(r,q^2)$ depending on a pair of parameters…
In these notes I proved the Chai-Faltings version of Eichler-Shimura congruence relation for simple GSpin Shimura varieties. This extends the results by Bueltel, Wedhorn and Koskivirta.
In this paper we consider a special class of arithmetic quotients of bounded symmetric domains which can roughly be described as higher- dimensional analogues of the Hilbert modular varities. The algebraic groups are defined as the unitary…
The Shimura correspondence connects modular forms of integral weights and half-integral weights. One of the directions is realized by the Shintani lift, where the inputs are holomorphic differentials and the outputs are holomorphic modular…
We study Shimura (special) subvarieties in the moduli space $A_{p,D}$ of complex abelian varieties of dimension $p$ and polarization type $D$. These subvarieties arise from families of covers compatible with a fixed group action on the base…
In this paper we recall the construction and basic properties of complex Shimura varieties and show that these properties actually characterize them. This characterization immediately implies the explicit form of Kazhdan's theorem on the…
Using the formalism of discrete quantum group gauge theory, one can construct the quantum algebras of observables for the Hamiltonian Chern-Simons model. The resulting moduli algebras provide quantizations of the algebra of functions on the…
Shimura curves are moduli spaces of abelian surfaces with quaternion multiplication. Models of Shimura curves are very important in number theory. Klein's icosahedral invariants $\mathfrak{A},\mathfrak{B}$ and $\mathfrak{C}$ give the…
We generalize a result of Ribet and Takahashi on the parametrization of elliptic curves by Shimura curves to the Hilbert modular setting. In particular, we study the behaviour of the parametrization of modular abelian varieties by Shimura…
A particular case of Bergeron-Venkatesh's conjecture predicts that torsion classes in the cohomology of Shimura varieties are rather rare. According to this and for Kottwitz-Harris-Taylor type of Shimura varieties, we first associate to…
We study the modularity of the generating series of special cycles on unitary Shimura varieties over CM-fields of degree $2d$ associated with a Hermitian form in $n+1$ variables whose signature is $(n,1)$ at $e$ real places and $(n+1,0)$ at…
Moore-Tachikawa varieties are certain Hamiltonian holomorphic symplectic varieties conjectured in the context of $2$-dimensional topological quantum field theories. We discuss several constructions related to these varieties.
We consider Shimura varieties associated to a unitary group of signature $(n-1, 1)$. For these varieties, we construct $p$-adic integral models over odd primes $p$ which ramify in the imaginary quadratic field with level subgroup at $p$…
In this paper we study the action of complex conjugation on Shimura varieties and the problem of descending these to the maximal totally real field of the reflex field. We prove the existence of such descent for many Shimura varieties whose…
We first give a relative flexible process to construct torsion cohomology classes for Shimura varieties of Kottwitz-Harris-Taylor type with coefficient in a non too regular local system. We then prove that associated to each torsion…
We compute the level groups associated with mixed Shimura varieties that appear at the boundaries of compactifications of Shimura varieties and show that the boundaries of minimal compactifications of Pappas-Rapoport integral models are…
The object of this work is to present the status of art of an open problem: to provide an analogue for Shimura curves of the Ihara's lemma \cite{Ihara73} which holds for modular curves. We will describe our direct result towards the…
In [1] some quotients of one-parameter families of Calabi-Yau varieties are related to the family of Mirror Quintics by using a construction due to Shioda. In this paper, we generalize this construction to a wider class of varieties. More…
Let $M$ be the Shimura variety associated to the group of spinor similitudes of a quadratic space over $\mathbb{Q}$ of signature $(n,2)$. We prove a conjecture of Bruinier and Yang, relating the arithmetic intersection multiplicities of…
We study the moduli space of twisted quasimaps from a fixed smooth projective curve to a Nakajima's quiver variety and the moduli space of $\delta$-stable framed twisted quiver bundles with moment map relations. We show that they carry…