17 citations · 63 across the 39 of their papers we have counts for
10 papers · 1 filter
Cup product of inhomogeneous Tate cochains, and Galois cohomology of tori over local fields that split over cyclic extensions
Mikhail Borovoi
In this note we give formulas for cup product in Tate cohomology in terms of inhomogeneous cochains. Using one of these formulas, for a torus T defined over a non-archimedean local…
Is there a group structure on the Galois cohomology of a reductive group over a global field?
Mikhail Borovoi
Let K be a global field, that is, a number field or a global function field. It is known that the answer to the question in the title over K is "Yes" when K has no real embeddings.…
Galois cohomology of reductive groups over global fields
Mikhail Borovoi, Tasho Kaletha, Vladimir Hinich
We give closed formulas for the abelian Galois cohomology groups H^1_{ab}(F,G) and H^2_{ab}(F,G) of a connected reductive group G over a global field F in terms of the algebraic fu…
Criterion for surjectivity of localization in Galois cohomology of a reductive group over a number field
Mikhail Borovoi, Zev Rosengarten
Let be a connected reductive group over a number field , and let be a set (finite or infinite) of places of . We give a necessary and sufficient condition for the sur…
Homogeneous spaces of Hilbert type
Mikhail Borovoi
Let k be a global field. Let G be a connected linear algebraic k-group, assumed reductive when k is a function field. It follows from a result of a preprint by Bary-Soroker, Fehm a…
A cohomological obstruction to weak approximation for homogeneous spaces
Mikhail Borovoi, Tomer M. Schlank
Let X be a homogeneous space, X = G/H, where G is a connected linear algebraic group over a number field k, and H is a k-subgroup of G (not necessarily connected). Let S be a finit…