Related papers: Arithmetic level raising for certain quaternionic …

We prove a conjectural formula relating the Bessel period of certain automorphic forms on $\mathrm{GSp}_4$ to a central $L$-value. This formula is proposed by Liu \cite{liu} as the refined Gan-Gross-Prasad conjecture for the groups…

We construct a moduli stack of rank 4 symplectic projective \'etale $(\varphi,\Gamma)$-modules and prove its geometric properties for any prime $p>2$ and finite extension $K/\mathbf{Q}_p$. When $K/\mathbf{Q}_p$ is unramified, we adapt the…

We give two proofs of a level-rank duality for braided fusion categories obtained from quantum groups of type $C$ at roots of unity. The first proof uses conformal embeddings, while the second uses a classification of braided fusion…

We formulate a refined version of the Birch and Swinnerton-Dyer conjecture for abelian varieties over global function fields. This refinement incorporates both families of congruences between the leading terms of Artin-Hasse-Weil $L$-series…

We extend the Cohen-Lenstra heuristics to the setting of ray class groups of imaginary quadratic number fields, viewed as exact sequences of Galois modules. By asymptotically estimating the mixed moments governing the distribution of a…

We generalize the prior linked symplectic Grassmannian construction, applying it to to prove smoothing results for rank-2 limit linear series with fixed special determinant on chains of curves. We apply this general machinery to prove new…

In this note, we study the superspecial loci of orthogonal type Shimura varieties of signature (n-2, 2) with n>3. We prove a conjecture of Gross on the parametrizations of the superspecial locus in the special fiber of an orthogonal type…

We study the question of the growth of Betti numbers of certain arithmetic varieties in tower of congruence coverings. In fact, our results are about Siegel varieties and varieties associated to orthogonal groups. We explain how a theorem…

We prove a precise formula relating the Bessel period of certain automorphic forms on ${\rm GSp}_{4}(\mathbb{A}_{F})$ to a central $L$-value. This is a special case of the refined Gan--Gross--Prasad conjecture for the groups $({\rm…

We prove a weighted Sato-Tate law for the Satake parameters of automorphic forms on $\rm{GSp}_4$ with respect to a fairly general congruence subgroup $H$ whose level tends to infinity. When the level is squarefree we refine our result to…

We consider the local model of a Shimura variety of PEL type, with the unitary similitudes corresponding to a ramified quadratic extension of $\mathbb{Q}_p$ as defining group. We examine the cases where the level structure at $p$ is given…

Let $G$ be the semidirect product $N \rtimes \mathbb{R}$, where $N$ is a stratified Lie group and $\mathbb{R}$ acts on $N$ via automorphic dilations. Homogeneous left-invariant sub-Laplacians on $N$ and $\mathbb{R}$ can be lifted to $G$,…

Symplectic 4-manifolds $(X,\omega)$ with $b_+{=}1$ are roughly classified by the canonical class $K$ and the symplectic form $\omega$ depending upon the sign of $K^2$ and $K\cdot \omega$. Examples are known for each category except for the…

In this paper we deduce a graded version of Quillen--Suslin's Local-Global Principle for the traditional classical groups, viz. general linear, symplectic and orthogonal groups and establish its equivalence of the normality property of the…

We construct explicit generating series of arithmetic extensions of Kudla's special divisors on integral models of unitary Shimura varieties over CM fields with arbitrary split levels and prove that they are modular forms valued in the…

Let $A$ be the Steenrod algebra over the finite field $k := \mathbb Z_2$ and $G(q)$ be the general linear group of rank $q$ over $k.$ A well-known open problem in algebraic topology is the explicit determination of the cohomology groups of…

We consider the degree 4 L-function associated to an automorphic representation of the symplectic group GSp(4). Starting with Beilinson's Eisenstien symbol we construct some motivic cohomology classes on the Shimura variety of GSp(4). We…

The formal degree conjecture relates the formal degree of an irreducible square-integrable representation of a reductive group over a local field to the special value of the adjoint $\gamma$-factor of its $L$-parameter. In this paper, we…

We prove two formulas in the style of the Gross-Zagier theorem, relating derivatives of L-functions to arithmetic intersection pairings on a unitary Shimura variety. We also prove a special case of Colmez's conjecture on the Faltings…

We study the characters induced by suitable level structures of abelian varieties with quaternionic multiplication following the methods of Mazur, Momose, who studied the characters induced by elliptic curves, and Arai--Momose, who studied…