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In this article, we construct in a purely local way partial (Hasse) invariants for $p$-divisible groups with given endomorphisms, using crystalline cohomology. Theses invariants generalises the classical Hasse invariant, and allow us to…
We introduce a notion of a group-partition for a finite Abelian group, which is a generalized notion of the standard partition. To obtain asymptoticdistributions of group-partition, we study the Dirichlet series for group-partitions by…
We introduce new invariants in equivariant birational geometry and study their relation to modular symbols and cohomology of arithmetic groups.
We prove a theorem giving the asymptotic number of binary quartic forms having bounded invariants; this extends, to the quartic case, the classical results of Gauss and Davenport in the quadratic and cubic cases, respectively. Our…
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)…
This article is a contribution to the classification of quadratically integrable systems with vector potentials whose integrals are of the nonstandard, nonseparable type. We focus on generalized parabolic cylindrical case, related to…
The aim of this paper is to give a new description of the geometry appearing in the multi-specialization along a general family of submanifolds of a real analytic manifold (including some important cases as clean intersection or a…
We construct explicit examples of cubic surfaces over $\bbQ$ such that the 27 lines are acted upon by the index two subgroup of the maximal possible Galois group. This is the simple group of order $25 920$. Our examples are given in…
We define a categorical framework in which we build a systematic construction that provides generic invariants for C*-algebras. The benefit is significant as we show that any invariant arising this way automatically enjoys nice properties…
We report on the computation of invariants, covariants, and contravariants of cubic surfaces. All algorithms are implemented in the computer algebra system magma.
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
Continuing the thrust of our recent work, but with an important new idea, we find a cut-off regularization of the determinant of a scalar particle in a classical Euclidean gravitational field. The field is assumed asymptotically flat, and…
Recently, a geometrical characterization of vector spaces served to generalize them into a new class of algebras. Instead of the algebraic properties of the underlying fields, we generalized the recently discovered property of such spaces…
We study the distribution of $2$-torsion in class groups and narrow class groups of cubic fields and cubic orders subject to prescribed shape conditions. The \emph{shape} of a cubic order in a number field is a natural geometric invariant…
We investigate the existence of coordinate transformations which bring a given vector field on a manifold equipped with an involutive distribution into the form of a second-order differential equation field with parameters. We define…
In this text, we explore the tools that Projective Differential Geometry can provide for the asymptotic analysis of classical fields on projectively compact manifolds. We emphasise on the case of order 2-compactifications and develop, in…
One can define class invariants for a quartic primitive CM field K as special values of certain Siegel (or Hilbert) modular functions at CM points corresponding to K. We provide explicit bounds on the primes appearing in the denominators of…
We study invariants under gauge transformations of linear partial differential operators on two variables. Using results of BK-factorization, we construct hierarchy of general invariants for operators of an arbitrary order. Properties of…
The category $\bcalNT$ is a category of certain commutative graded algebras over a field. It was introduced in \cite{Lobos2} as a generalization of algebras generated by Jucys-Murphy elements in the many \textbf{End} algebras of the…
We give an elementary algebraic proof of some asymptotic estimates (called by Demailly asymptotic Morse inequalities) for the dimensions of cohomology groups of the difference of two ample line bundles on a smooth complex projective variety…