40 citations · 281 across the 31 of their papers we have counts for
21 papers · 1 filter
Formal Bott-Thurston cocycle and part of a formal Riemann-Roch theorem
D. V. Osipov
The Bott-Thurston cocycle is a -cocycle on the group of orientation-preserving diffeomorphisms of the circle. We introduce and study a formal analog of Bott-Thurston cocycle. Th…
Arithmetic surfaces and adelic quotient groups
D. V. Osipov
We explicitly calculate an arithmetic adelic quotient group for a locally free sheaf on an arithmetic surface when the fiber over the infinite point of the base is taken into accou…
Second Chern numbers of vector bundles and higher adeles
D. V. Osipov
We give a construction of the second Chern number of a vector bundle over a smooth projective surface by means of adelic transition matrices for the vector bundle. The construction…
On adelic quotient group for algebraic surface
D. V. Osipov
We calculate explicitly an adelic quotient group for an excellent Noetherian normal integral two-dimensional separated scheme. An application to an irreducible normal projective al…
Higher-dimensional Contou-Carrère symbol and continuous automorphisms
Sergey Gorchinskiy, Denis Osipov
We prove that the higher-dimensional Contou-Carrère symbol is invariant under continuous automorphisms of algebras of iterated Laurent series over a ring. Applying this property, w…
A higher-dimensional Contou-Carrère symbol: local theory
Sergey Gorchinskiy, Denis Osipov
We construct a higher-dimensional Contou-Carrère symbol and we study its various fundamental properties. The higher-dimensional Contou-Carrère symbol is defined by means of the bou…