Related papers: Good reduction, bad reduction
The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. All possible reductions of these equations to…
We give bounds on the primes of geometric bad reduction for curves of genus three of primitive CM type in terms of the CM orders. In the case of genus one, there are no primes of geometric bad reduction because CM elliptic curves are CM…
A somewhat pretentious presentation of number systems (N, Z, Q, R, C, Q_p, >...). The problem of a p-adic characterisation of good-reduction p-adic curves is posed.
We make a study of unipotent elements in a connected reductive group over an algebraically closed field with emphasis on the case where the characteristic is a bad prime. We try to see how much of the theory of Dynkin-Kostant extends to…
We prove the vanishing of certain low degree cohomologies of some induced representations. As an application, we determine certain low degree cohomologies of congruence groups.
We give a good reduction criterion for proper polycurves with sections,i.e., successive extensions of family of curves with section, under mild assumption. This criterion is a higher dimensional version of the good reduction criterion for…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
We give examples of spaces which are good and bad at different primes in the sense of Bousfield and Kan in any arbitrary combination and investigate which impact the existence of a Sylow $p$-subgroup has on the homotopy type on the…
Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal…
Data generated in the fields of science, technology, business and in many other fields of research are increasing in an exponential rate. The way to extract knowledge from a huge set of data is a challenging task. This paper aims to propose…
The un-reduction procedure introduced previously in the context of Mechanics is extended to covariant Field Theory. The new covariant un-reduction procedure is applied to the problem of shape matching of images which depend on more than one…
Let $R$ be a commutative unital ring, $a\in R$ and $t$ a positive integer. $a^{t}$-reduced $R$-modules and universally $a^{t}$-reduced $R$-modules are defined and their properties given. Known (resp. new) results about reduced $R$-modules…
We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective of this article is to establish fundamental properties of…
This is a revision and update of the part of the preprint math.CO/0405210 concerning field coefficients, line complexes, and the Hessian arrangement. The material from that paper concerning coefficients in arbitrary commutative rings and…
We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic…
This paper addresses weak approximation for rationally connected varieties defined over the function field of a curve, especially at places of bad reduction. Our approach entails analyzing the rational connectivity of the smooth locus of…
Ax gave examples of fields of cohomological dimension 1 which are not C_1-fields. Kato and Kuzumaki asked whether a weak form of the C_1-property holds for all fields of cohomological dimension 1 (existence of solutions in extensions of…
The reduction algorithm is used to compute reduced ideals of a number field. However, there are reduced ideals that can never be obtained from this algorithm. In this paper, we will show that these ideals have inverses of larger norms among…
We study a mechanism of symmetry reduction in a higher-dimensional field theory upon orbifold compactification. Split multiplets appear unless all components in a multiplet of a symmetry group have a common parity on an orbifold. A gauge…
We study the special fibers of a certain class of absolutely simple abelian varieties over number fields with endomorphism rings $\bz$ and possessing $l$-adic monodromy groups of the least possible rank. We also study the Dirichlet density…