54 citations · 234 across the 25 of their papers we have counts for
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Orthogonal to principal ideles
Sergey Gorchinskiy
We describe the orthogonal to the group of principal ideles with respect to the global tame symbol pairing on the group of ideles of a smooth projective algebraic curve over a fiel…
Categorical measures for finite group actions
Daniel Bergh, Sergey Gorchinskiy, Michael Larsen +1
Given a variety with a finite group action, we compare its equivariant categorical measure, that is, the categorical measure of the corresponding quotient stack, and the categorica…
Integral Chow motives of threefolds with -motives of unit type
Sergey Gorchinskiy
We prove that if a smooth projective algebraic variety of dimension less or equal to three has a unit type integral -motive, then its integral Chow motive is of Lefschetz type.…
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…
Unramified Brauer group and its applications
Sergey Gorchinskiy, Constantin Shramov
This is a textbook on arithmetic geometry with special regard to unramified Brauer groups of algebraic varieties. The topics include Galois cohomology, Brauer groups, obstructions…
Tangent space to Milnor -groups of rings
S. O. Gorchinskiy, D. V. Osipov
We prove that the tangent space to the -th Milnor -group of a ring is isomorphic to group of -th absolute Kähler differentials of when the ring contains $\…