1
$\begingroup$

Let $X$ be a complex analytic manifold and let $\mathcal{M}$ be an integrable connection on $X$, i.e. a $\mathcal{D}_X$-module which happens to be coherent as an $\mathcal{O}_X$-module. If $U$ is any open subset of $X$ then $\mathcal{M}_{|U}$ is an integrable connection on $U$.

Suppose that $\mathcal{M}$ is irreducible and $U$ is connected. Must $\mathcal{M}_{|U}$ also be irreducible?

Improve this question
$\endgroup$
1
  • 4
    $\begingroup$ What if $\mathcal{M}$ comes from an irreducible representation of the fundamental group of $X$, yet $U$ is simply connected (a polydisk, say)? $\endgroup$
    – Jason Starr
    Commented Jan 16, 2016 at 17:24

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .