Table of contents

The space of all Γ-extensions of a given algebraic number field is considered. The behavior of certain invariants of Γ-extensions as functions on this space is studied by methods of commutative algebra. Bibliography: 4 titles.

The classical Cartan duality gives a classification of real forms of a complex semisimple Lie group by means of a classification of involutions of its compact real form. In the present article an analogous construction is given over p-adic fields. Bibliography: 8 titles.

This paper is devoted to the generalization of the theory of distributions (adeles) on schemes of dimension 2. Bibliography: 11 titles.

In this paper we consider homomorphisms of abelian schemes over a connected smooth algebraic curve defined over the field of complex numbers. We prove that under certain natural conditions the canonical map

is an isomorphism. Bibliography: 5 titles.

In this paper we show how to compute the Jordan decomposition of the monodromy of a one-parameter family of curves or surfaces in terms of the homology of the special fiber. Bibliography: 16 titles.

Let G be a connected Lie group, with Lie algebra which is the real form of the second category of type D_n. This paper lists all the connected closed subgroups U of G such that there exists a complex structure on the manifold M = G/U which is invariant under G, and it also describes all such structures on M. Bibliography: 7 titles.

In this article the author proves that the values of the multiplicative genera A_k under discussion, where K = 2, 3,..., are obstructions to the existence of nontrivial S¹-actions on a unitary manifold whose first Chern class is divisible by k. The effective computation of these obstructions is carried out for algebraic manifolds. Simultaneously, formulas for the bordism class of a ramified covering are obtained. Bibliography: 8 titles.

We prove a theorem on the structure of weakly closed reductive operator algebras. The proof essentially relies on a known result of V. I. Lomonosov on transitive operator algebras containing a nonzero compact operator. We deduce a number of corollaries which apply to the reductivity problem. Bibliography: 20 titles.

This paper obtains a normal form for formal series and for germs of smooth mappings with respect to the action of a group. In particular, this yields a more precise version of the "resonance" normal form for differential equations. It is proved that under the action of a given group of -mappings of coordinates any -germ can be reduced to the sum of two germs, of which one is in normal form and the other has zero Taylor series at the origin. Bibliography: 10 titles.

We consider inequalities of the form

(*)

where is an arbitrary majorant of the function . The set of parameters , , , , for which the inequalities (*) hold is described. Various generalizations of these inequalities are given. Bibliography: 22 titles.

A solution of the oblique derivative problem for a second order equation with coefficients having discontinuities of power order is determined in explicit form under minimal smoothness, and its properties are studied near the boundary and the point of degeneracy. Bibliography: 12 titles.

The paper gives a complete formulation and proof of a number of assertions regarding the point spectrum of the Schrödinger operator of a many-particle system announced earlier by the author. In particular, conditions that the discrete spectrum of this operator be finite are obtained. The results of the work are applicable to certain specific quantum systems, for example, to univalent negative atomic ions and to diatomic molecules. Bibliography: 20 titles.