Related papers: Mass formula for supersingular abelian surfaces

We examine the Chern class map ${c}_{1}: {\rm NS}(S)/p{\rm NS}(S) \rightarrow {\rm H}^{1}(S, \Omega^{1}_{S})$ for an abelian surface $S$ in characteristic $p \geq 3$, and give a basis of the kernel $c_{1}$ for the superspecial abelian…

For a local field with finite residue field of characteristique p, we give some refinements of Serre's mass formula in degree p which allow us to compute for example the contribution of cyclic extensions, or of those whose galoisian closure…

We derive an explicit formula for the volume of a regular simplex in the hyperbolic space of any dimension.

We prove that there exists a supersingular nonsingular curve of genus $4$ in arbitrary characteristic $p$. For $p>3$ we shall prove that the desingularization of a certain fiber product over $\mathbb{P}^1$ of two supersingular elliptic…

Let $F$ be a totally real field with ring of integers $O_F$, and $D$ be a totally definite quaternion algebra over $F$. A well-known formula established by Eichler and then extended by K\"orner computes the class number of any $O_F$-order…

We prove the modularity of a positive proportion of abelian surfaces over $\mathbf{Q}$. More precisely, we prove the modularity of abelian surfaces which are ordinary at $3$ and are $3$-distinguished, subject to some assumptions on the…

We exhibit a basis for the space of spherical characters of a distinguished supercuspidal representation $\pi$ of a connected reductive $p$-adic group, subject to the assumption that $\pi$ is obtained via induction from a representation of…

We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…

We classify isoparametric hypersurfaces in complex hyperbolic spaces.

We study the surface area of an ellipsoid in n-dimensional Euclidean space as the function of the lengths of their major semi-axes. We write down an explicit formula as an integral over the unit sphere, use the formula to derive convexity…

We classify smooth projective surfaces that are quotients of abelian surfaces by finite groups.

We establish a character formula for admissible unitary representations of $p$-adic almost algebraic solvable groups and we deduce the Plancherel measure in the unimodular case.

We propose a unitary matrix formulation of type IIB matrix model. One-loop effective action of the model exhibits supersymmetry for BPS background in the large N limit.

In this paper, we consider whether existence of a sums-of-squares formula depends on the base field. We reformulate the question of existence as a question in algebraic geometry. We show that, for large enough p, existence of…

We derive the Smarr formula for a five-dimensional spacetime which has a magnetic "bolt" in its center and is asymptotically R^(3,1) x S^1. Supersymmetry - and so the BPS-bound - is broken by the holonomy. We show how each topological…

We propose three kinds of explicit formulas for the elliptic lambda function by the elliptic modular function. Further, we derive incredible cubic identities as a corollary of our explicit formulas and evaluate some singular values of the…

In this paper we obtain an explicit formula for the higher Schur-multiplicator of an arbitrary finite abelian group with respect to the variety of nilpotent groups of class at most $c\geq 1$ .

Given an abelian surface $A$, defined over a discrete valuation field and having good reduction, does the attached Kummer surface $\mathrm{Km}(A)$ also have good reduction? In this paper we give an affirmative answer in the extreme case,…

We prove that any abelian surface defined over $\Q$ of $GL_2$-type having quaternionic multiplication and good reduction at 3 is modular. We generalize the result to higher dimensional abelian varieties with ``sufficiently many…

This paper is about one dimensional families of cyclic covers of the projective line in positive characteristic. For each such family, we study the mass formula for the number of non-ordinary curves in the family. We prove two equations for…