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Results tagged with nonabelian-cohomology
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user 4149
1
vote
Accepted
Connecting homomorphism in non-abelian cohomology
$\newcommand{\diag}{{\rm diag}}
\newcommand{\sH}{{\mathcal H}}
\newcommand{\R}{{\mathbb R}}
\newcommand{\HH}{\sf H}
\newcommand{\V}{{\sf V}}
\newcommand{\B}{{\sf B}}
\newcommand{\C}{{\Bbb C}}
$No, th …
- 14.2k
3
votes
Minimal parabolic subgroups are $G(k)$-conjugate: a cohomological interpretation?
For simplicity we write $G$ for $G^{\rm der}$ and $M_0$ for $M_0^{\rm der}$, then $G$ is a connected reductive group, and $M_0$ is a Levi subgroup of a minimal parabolic $P_0$ of $G$.
Let $$\xi\in{\rm …
- 14.2k
6
votes
Accepted
Non-abelian Ext functor and non-abelian $H^2$
EDITED, taking into account the comments of Donu Arapura.
As JLA wrote, a homomorphism $f\colon G\to N$ gives an extension
\begin{equation}\label{e:E}
1\to K\to E\to G\to 1.\tag{E}
\end{equation}
This …
- 14.2k
5
votes
Second nonabelian group cohomology: cocycles vs. gerbes
Nonabelian $H^2$ in Galois cohomology can be defined in terms of: (1) cocycles, (2) extensions, (3) gerbes. The relations between these three definitions are described in Section 2.2 of Le principe de …
- 14.2k