Related papers: Possible connection between a generalized Maeda's …

Let p be a prime and F a totally real field in which p is unramified. We consider mod p Hilbert modular forms for F, defined as sections of automorphic line bundles on Hilbert modular varieties of level prime to p in characteristic p. For a…

We study the generalized theta lifting between the double covers of split special orthogonal groups, which uses the non-minimal theta representations constructed by Bump, Friedberg and Ginzburg. We focus on the theta liftings of non-generic…

The aim of this article is to introduce Vogel's localization theorem for classes of D-complexes: this generalization of Waldhausen's localization theorem is especially useful and powerful in that it gives an explicit and computable…

By using techniques of holomorphic jets and Jacobian fields, we devise a non-equidistribution theory of holomorphic curves into complex projective varieties intersecting normal crossing divisors. Based on this theory established, we prove…

We investigate specializations of infinite families of regular Galois extensions over number fields. The problem to what extent the local behaviour of specializations of one single regular Galois extension can be prescribed has been…

Mitchell and Littlejohn showed that isotropy groups and orbits for $N$-body problems attain a sense of genericity for $N = 5$. The author recently showed that the arbitrary-$d$ generalization of this 3-$d$ result is that genericity in this…

A generalization of the two-dimensional Yang-Mills and generalized Yang-Mills theory is introduced in which the building B-F theory is nonlocal in the auxiliary field. The classical and quantum properties of this nonlocal generalization are…

An exterior differential calculus in the general framework of generalized Lie algebroids is presented. A theorem of Maurer-Cartan type is obtained. All results with details proofs are presented and a new point of view over exterior…

We study the minimal number of ramified primes in Galois extensions of rational function fields over finite fields with prescribed finite Galois group. In particular, we obtain a general conjecture in analogy with the well studied case of…

We present a quantitative version of Bilu's theorem on the limit distribution of Galois orbits of sequences of points of small height in the $N$-dimensional algebraic torus. Our result gives, for a given point, an explicit bound for the…

Let $X$ be a smooth projective variety defined on a finite field $\mathbb{F}_q$. On $X$ there is a special morphism $Fr_X$, which raises coordinates to exponent $q$: $t\mapsto t^q$. The two main results in this paper are: Result 1: If…

This paper is devoted to abelian varieties arising from generalized Legendre curves. In particular, we consider their corresponding Galois representations, periods, and endomorphism algebras. For certain one parameter families of…

Recently continuous rational maps between real algebraic varieties have attracted the attention of several researchers. In this paper we continue the investigation of approximation properties of continuous rational maps with values in…

Galileon models arise in certain braneworld scenarios as modifications to General Relativity, and are also interesting as field theories in their own right. We show how the galileon model can be naturally generalized to include local gauge…

We discuss one family of possible generalizations of the Jaynes-Cummings and the Tavis-Cummings models using the technique of algebraic Bethe ansatz related to the Gaudin-type models. In particular, we present a family of (generically)…

In the basic general frame of the Langlands global program, a local p-adic elliptic semimodule corresponding to a local (left) cuspidal form is constructed from its global equivalent covered by p-th roots. In the same context, global and…

We describe a generalization of the large sieve to situations where the underlying groups are nonabelian, and give several applications to the arithmetic of abelian varieties. In our applications, we sieve the set of primes via the system…

Let F be an unramified extension of Qp. The first aim of this work is to develop a purely local method to compute the potentially Barsotti-Tate deformations rings with tame Galois type of irreducible two-dimensional representations of the…

In this paper, we consider infinite Galois extensions of number fields and study the relation between their local degrees and the structure of their Galois groups. It is known that, if $K$ is a number field and $L/K$ is an infinite Galois…

A central conjecture in inverse Galois theory, proposed by D\`{e}bes and Deschamps, asserts that every finite split embedding problem over an arbitrary field can be regularly solved. We give an unconditional proof of a consequence of this…