In mathematics, the local invariant cycle theorem was originally a conjecture of Griffiths[1][2] which states that, given a surjective proper map
to the unit disk that has maximal rank everywhere except over 0, each cohomology class on
is the restriction of some cohomology class on the entire
if the cohomology class is invariant under a circle action (monodromy action); in short, is surjective.
The conjecture was first proved by Clemens.
The theorem is also a consequence of the BBD decomposition.
[3] Deligne also proved the following.
[4][5] Given a proper morphism
an algebraically closed field, if
is essentially smooth over
are the special and generic points and the homomorphism is the composition
This algebraic geometry–related article is a stub.