Abelian Varieties, l-adic Representations and Lie Algebras.
A finiteness theorem for unpolarized Abelian varieties over number fields with prescribed places of bad reduction.
On the perturbation propagation in the initial-boundary value problem for quasilinear first order equations.
The paper deals with initial-boundary value problem for generalized solutions of single quasilinear nonautonomous conservation law. For the case so-called "processes with aggravation" the localization property and inner boundedness are studied. Also in case when boundary function tends to zero as t ⇒ +∞ the localization effect is regarded.
On the nonhamiltonian character of shocks in 2-D pressureless gas
The paper deals with the 2-D system of gas dynamics without pressure which was introduced in 1970 by Ua. Zeldovich to describe the formation of largescale structure of the Universe. Such system occurs to be an intermediate object between the systems of ordinary differential equations and hyperbolic systems of PDE. The main its feature is the arising of singularities: discontinuities for velocity and d-functions of various types for density. The rigorous notion of generalized solutions in terms of...
On the behaviour of generalized solutions to genuinely nonlinear first order equations for small and large values of time.
The paper deals with the asymptotic behavior of generalized solutions to nonlinear first order equations. With the aid of explicit variational representation one studies the decrease of solutions for a large time. And for the small time an asymptotic of the perturbation?s front is calculated.
On the behaviour of generalized solutions of the Cauchy problem for essentially nonautonous quasilinear first order equations.
A two-component copula with links to insurance
This paper presents a new copula to model dependencies between insurance entities, by considering how insurance entities are affected by both macro and micro factors. The model used to build the copula assumes that the insurance losses of two companies or lines of business are related through a random common loss factor which is then multiplied by an individual random company factor to get the total loss amounts. The new two-component copula is not Archimedean and it extends the toolkit of copulas...
Connectedness results for -adic representations associated to abelian varieties
Étale cohomology and reduction of abelian varieties
In this paper we study the étale cohomology groups associated to abelian varieties. We obtain necessary and sufficient conditions for an abelian variety to have semistable reduction (or purely additive reduction which becomes semistable over a quadratic extension) in terms of the action of the absolute inertia group on the étale cohomology groups with finite coefficients.
O situaci v sibiřské matematice
About Sergej L'vovich Sobolev.
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