The concept of an n-dimensional local field was introduced by A.N. Parshin [Pa1] with the aim of generalizing the classical adelic formalism to (absolutely) ndimensional schemes. By definition, aâ€¦ (More)

We develop a harmonic analysis on objects of some category C 2 of infinite-dimensional filtered vector spaces over a finite field. It includes two-dimensional local fields and adelic spaces ofâ€¦ (More)

Example. Let X be an algebraic projective irreducible surface over a field k and let P be a closed point of X , C âŠ‚ X be an irreducible curve such that P âˆˆ C . If X and C are smooth at P , then weâ€¦ (More)

This paper suggests a new approach to the study of the fundamental properties of the zeta function of a model of elliptic curve over a global field. This complex valued commutative approach is aâ€¦ (More)

In 70's there was discovered a construction how to attach to some algebraic-geometric data an infinite-dimensional subspace in the space k((z)) of the Laurent power series. The construction wasâ€¦ (More)

Example. Let X be an algebraic projective irreducible surface over a field k and let P be a closed point of X , C âŠ‚ X be an irreducible curve such that P âˆˆ C . If X andC are smooth atP , then we lettâ€¦ (More)

In this paper we introduce new various generalizations of the classical Kadomtsev-Petviashvili hierarchy in the case of operators in several variables. These generalizations are the candidates forâ€¦ (More)

In algebraic geometry, there exist cohomologies of coherent sheaves on algebraic varieties. So the following natural question arises: what is the Lefschetz number Lef(X,F , f) = âˆ‘n i=0(âˆ’1) Tr(fâ€¦ (More)

In the sixties Mazur and Manin pointed out intriguing analogies between prime ideals in number rings and knots in 3-manifolds. Let us recall some of the relevant ideas. In many respects the spectrumâ€¦ (More)