Related papers: On Bost-Connes type systems and Complex Multiplica…
We give an algorithm to compute representatives of the conjugacy classes of semisimple square integral matrices with given minimal and characteristic polynomials. We also give an algorithm to compute the $\mathbb{F}_q$-isomorphism classes…
We derive a discrete analogue of Morse-Bott theory on CW complexes and use this discrete Morse-Bott function to do some Conley theory analysis. It turns out that our discrete Morse-Bott theory is indeed a generalization of Forman's discrete…
In this paper, we provide a classification of certain points on Hilbert modular varieties over finite fields under a mild assumption on Newton polygon. Furthermore, we use this characterization to prove estimates for the size of isogeny…
We present a new notion of speciality which is valid for Bohr - Sommerfeld lagrangian submanifolds. For algebraic varieties it leads to the construction of finite dimensional moduli spaces which are algebraic starting with any ample line…
In this article we make an explicit approach to the higher degree case of the problem: " For a given $CM$ field $M$, construct its maximal abelian extension $C(M)$ (i.e. the Hilbert class field) by the adjunction of special values of…
We introduce an algorithm that computes explicit class fields of an imaginary quadratic field $K$ for a given modulus $\mathfrak{f}\subset\mathcal{O}_K$ more efficiently than the use of their classical counterparts. Therein, we prove the…
We build models using an indiscernible model sub-structures of ${\kappa} \ge {\lambda}$ and related more complicated structures. We use this to build various Boolean algebras.
Using the superconformal (SC) indices techniques, we construct Seiberg type dualities for $\mathcal{N}=1$ supersymmetric field theories outside the conformal windows. These theories are physically distinguished by the presence of chiral…
We study the combinatorics of hyperplane arrangements over arbitrary fields. Specifically, we determine in which situation an arrangement and its reduction modulo a prime number have isomorphic lattices via the use of minimal strong…
We work out the construction of a Stein manifold from a commutative Arens-Michael algebra, under assumptions that are mild enough for the process to be useful in practice. Then, we do the passage to arbitrary complex manifolds by proposing…
Let A be a CM abelian variety defined over a number field K. We compute congruence relations on units in fields generated by adjoining torsion points of A to K. For elliptic curves, congruence relations of the type we compute were used in…
We construct an Euler system attached to a weight 2 modular form twisted by a Groessencharacter of an imaginary quadratic field, and apply this to bounding Selmer groups.
Following Hasse's example, various authors have been deriving divisibility properties of minus class numbers of cyclotomic fields by carefully examining the analytic class number formula. In this paper we will show how to generalize these…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
We show how to use divisors on the projectivized Hodge bundle to construct special vector-valued modular forms and then apply invariant theory to construct all vector-valued Siegel modular forms of level two and degree two. Thus we…
Support varieties for any finite dimensional algebra over a field were introduced by Snashall-Solberg using graded subalgebras of the Hochschild cohomology. We mainly study these varieties for selfinjective algebras under appropriate finite…
We introduce a method to construct special holomorphic tensors on orthogonal modular varieties from scalar-valued modular forms, and give applications to the Lang conjecture on the birational type of subvarieties of orthogonal modular…
We present a new application of multi-orbit cyclic subspace codes to construct large optical orthogonal codes, with the aid of the multiplicative structure of finite fields extensions. This approach is different from earlier approaches…
We show that conjugation by an automorphism of the complex numbers (as an abstract field) may change the topological fundamental group of a locally symmetric variety over C. As a consequence, we obtain a large class of algebraic varieties…
A classification of semisimple algebras of vector fields on C^N that have a Cartan subalgebra of dimension N is given. The proof uses basic representation theory and the local canonical form of semisimple Lie algebras of vector fields.