Related papers: On the modularity level of modular abelian varieti…

Let $G$ be a connected reductive group over an algebraically closed field of characteristic $p>0$. Given an indecomposable G-module $M$, one can ask when it remains indecomposable upon restriction to the Frobenius kernel $G_r$, and when its…

Let $p$ be an unramified prime in a totally real field $L$ such that $h^+(L)=1$. Our main result shows that Hilbert modular newforms of parallel weight two for $\Gamma_0(p)$ can be constructed naturally, via classical theta series, from…

In this paper, we study the simple modules for the restricted Lie superalgebra $gl(m|n)$. A condition for the simplicity of the induced modules is given, and an analogue of Kac-Weisfeiler theorem is proved.

Let $R$ be a commutative ring. Roughly speaking, we prove that an $R$-module $M$ is flat iff it is a direct limit of $R$-module affine algebraic varieties, and $M$ is a flat Mittag-Leffler module iff it is the union of its $R$-submodule…

Let B be a commutative B\'ezout domain B and let MSpec(B) be the maximal spectrum of B. We obtain a Feferman-Vaught type theorem for the class of B-modules. We analyse the definable sets in terms, on one hand, of the definable sets in the…

Let $K$ be an imaginary quadratic field with discriminant $d_K\leq-7$. We deal with problems of constructing normal bases between abelian extensions of $K$ by making use of singular values of Siegel functions. First, we show that a…

Let $K$ be a field which is complete for a discrete valuation. We prove a logarithmic version of the N\'eron-Ogg-Shafarevich criterion: if $A$ is an abelian variety over $K$ which is cohomologically tame, then $A$ has good reduction in the…

We consider the general problem of deforming a surjective map of modules $f : E \to F$ over a coproduct sheaf of rings $B=B_1 \otimes_A B_2$ when the domain module $E = B_1 \otimes_A E_2$ is obtained via extension of scalars from a…

We classify all $n$-dimensional reduced Cohen-Macaulay modular quotient variety $\mathbb{A}_\mathbb{F}^n/C_{2p}$ and study their singularities, where $p$ is a prime number and $C_{2p}$ denotes the cyclic group of order $2p$. In particular,…

We study the possible weights of an irreducible two-dimensional mod p representation of the absolute Galois group of F which is modular in the sense of that it comes from an automorphic form on a definite quaternion algebra with centre F…

Motivated by the problem of determining the structure of integral points on subvarieties of semiabelian varieties defined over finite fields, we prove a quantifier elimination result for certain modules over finite simple extensions of the…

Let $f\colon X\to\mathbb{A}^1_k$ be a morphism from a smooth variety to an affine line with an isolated singular point. For such a singularity, we have two invariants. One is a non-degenerate symmetric bilinear form (de Rham), and the other…

The propagator of linear molecules whose constituents interact through oscillator potentials can be obtained in a closed form for $N$ atoms as long as $N \leq 4$. We compute the propagator for arbitrary $N$ in the approximation $N \gg 1$.…

We first investigate the algebraic structure of vertex algebroids $B$ when $B$ are simple Leibniz algebras. Next, we use these vertex algebroids $B$ to construct indecomposable non-simple $C_2$-cofinite $\mathbb{N}$-graded vertex algebras…

We investigate the join semilattice of modal operators on a Boolean algebra $B$. Furthermore, we consider pairs $(f,g)$ of modal operators whose supremum is the unary discriminator on $B$, and study the associated bi--modal algebras.

We study the cone of moving divisors on the moduli space ${\mathcal A}_g$ of principally polarized abelian varieties. Partly motivated by the generalized Rankin-Cohen bracket, we construct a non-linear holomorphic differential operator that…

Let $p$ be a prime number and $N$ an integer prime to $p$. We show that the operator $U_p$ on the space of cuspidal modular forms of level $pN$ and weight two is semi-simple. It follows from this that the Hecke algebra acting on the space…

We prove that for every field k and every positive integer n, there exists an absolutely simple n-dimensional abelian variety over k. We also prove an asymptotic result for finite fields: For every finite field k and positive integer n, we…

Let $U/L$ be a finite abelian extension of number fields. We first construct a universal primitive generator of $U$ over $L$ whose relative trace to any intermediate field $F$ becomes a generator of $F$ over $L$, too. We also develop a…

We present a new formulation to calculate the electric conductance of mesoscopic conductors by utilizing the singular value decomposition, which is a mathematical technique to manipulate matrices. Our formulation is useful in treating…