7 papers
Constructing a complex Lie algebra isomorphic to its complex conjugate but not definable over reals
Mikhail Borovoi, Willem A. de Graaf, Robert M. Guralnick
Following an idea of Demarche and using computer calculations of the authors and ideas of LLM Claude Fable, we construct an explicit 10-dimensional complex two-step nilpotent Lie a…
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…
Non-abelian hypercohomology of a group with coefficients in a crossed module, and Galois cohomology
Mikhail Borovoi
We develop a hypercohomology theory of a group with coefficients in a crossed module, and apply it to define abelianization maps for Galois cohomology of reductive algebraic groups…
Nonabelian with coefficients in a group and with coefficients in a crossed module
Mikhail Borovoi
In this note, following Dedecker and Debremaeker, we extend the cohomology exact sequence for nonabelian , using nonabelian with coefficients in crossed modules.
The defect of weak approximation for a reductive group over a global field
Mikhail Borovoi, Jean-Louis Colliot-Thélène
We compute the defect of weak approximation for a reductive group G over a global field K in terms of the algebraic fundamental group of G.
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…