I´m beginner in sheaf theory, and I´m stuck with this property
Thank your for you time
$\begingroup$
$\endgroup$
0
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
(This was meant to be a comment, but matrices don't seem to display properly there.)
This is just a hint. If you set things up properly, the 1-cocycle for $\mathcal{E}$ has the form $ g_{ij}=\begin{pmatrix} g_{ij}' & f_{ij}\\ 0 & g_{ij}''\end{pmatrix}$ where the diagonal entries are the cocycles for the other two sheaves. Then $\det g_{ij}= \det g_{ij}'\det g_{ij}''$ implies what you want.
answered Dec 16, 2017 at 20:10