17 citations · 63 across the 39 of their papers we have counts for
47 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 the LLM Claude Fable 5, we construct an explicit 10-dimensional complex two-step nilpotent…
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…
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.…
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.
Real non-degenerate two-step nilpotent Lie algebras of dimension eight
Mikhail Borovoi, Bogdan Adrian Dina, Willem A. de Graaf
We classify the non-degenerate two-step nilpotent Lie algebras of dimension 8 over the field of real numbers, using known results over complex numbers. We write explicit structure…