Related papers: Higher theta series for unitary groups over functi…

In this paper we investigate a result of Ueno on the modularity of generating series associated to the zeta functions of binary Hermitian forms previously studied by Elstrodt et al. We improve his result by showing that the generating…

A natural explicit condition is given ensuring that an action of the multiplicative monoid of non-negative reals on a manifold F comes from homotheties of a vector bundle structure on F, or, equivalently, from an Euler vector field. This is…

We study fundamental groups of algebraic stacks. We show that these fundamental groups carry an additional structure coming from the inertia groups. Then use this additional structure to analyze geometric/ topological properties of stacks.…

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…

We suggest a construction of virtual fundamental classes of certain types of moduli spaces.

Heegner cycles are higher weight analogues of Heegner points. Their arithmetic intersection numbers also appear as Fourier coefficients of modular forms and often belong to abelian extensions of imaginary-quadratic fields. Rotger and Seveso…

We derive finite rational formulas for the traces of cycle integrals of certain meromorphic modular forms. Moreover, we prove the modularity of a completion of the generating function of such traces. The theoretical framework for these…

We study the bundles of generalized theta functions constructed from moduli spaces of sheaves over abelian surfaces. In degree 0, the splitting type of these bundles is expressed in terms of indecomposable semihomogeneous factors.…

We shall show that the stable categories of graded Cohen-Macaulay modules over quotient singularities have tilting objects. In particular, these categories are triangle equivalent to derived categories of finite dimensional algebras. Our…

Persistence modules are representations of products of totally ordered sets in the category of vector spaces. They appear naturally in the representation theory of algebras, but in recent years they have also found applications in other…

Boij-S\"oderberg theory gives a combinatorial description of the set of Betti tables belonging to finite length modules over the polynomial ring $S = k[x_1, \ldots, x_n]$. We posit that a similar combinatorial description can be given for…

In this paper we give some evidence for the Tate (and Hodge) conjecture(s) for a class of Hilbert modular fourfolds X, whose connected components arise as arithmetic quotients of the fourfold product of the upper half plane by congruence…

We study special cycles on a Shimura variety of orthogonal type over a totally real field of degree $d$ associated with a quadratic form in $n+2$ variables whose signature is $(n,2)$ at $e$ real places and $(n+2,0)$ at the remaining $d-e$…

In this note, we study the arithmetic nature of values of modular functions, meromorphic modular forms and meromorphic quasi-modular forms with respect to arbitrary congruence subgroups, that have algebraic Fourier coefficients. This…

In this paper, we complete the proof of the conjecture of Gross and Zagier concerning algebraicity of higher Green functions at a single CM point on the product of modular curves. The new ingredient is an analogue of the incoherent…

We show that indefinite theta series on cones converge and provide an explicit modular completion. Our completion rests on a convolution of the Gaussian with a piecewise constant function supported on the cone. Our main innovation is to…

The aim of the research presented in this paper is to derive the systems of ordinary differential equations (ODEs) satisfied by modular forms of level six and to construct extensions of the differential field of the cubic theta functions,…

We introduce and investigate an infinite family of functions which are shown to have generalised quantum modular properties. We realise their "companions" in the lower half plane both as double Eichler integrals and as non-holomorphic theta…

We prove that, over an arbitrary CM field, every symmetric formal Fourier-Jacobi series converges and equals the Fourier-Jacobi expansion of a genuine Hermitian Hilbert modular form. As an application, we show that the Chow-valued Kudla…

In this article, we relate the fake special cycle classes $z_{\mathbb{L}_{\sigma},r}$ attached to a Hecke eigensheaf $\mathbb{L}_{\sigma}\in\mathrm{Shv}_{\mathrm{Nilp}}(\mathrm{Bun}_G)$ introduced in the author's previous work to the…