2007-02-16
T. N. Venkataramana, Tata Institute
Jordan Decomposition in lattices and quasi-unipotence of
monodromy
We prove that the semi-simple and unipotent parts of an element of a
lattice in a semi-simple Lie group virtually belong to the lattice;
this can be used to prove that under a holomorphic map from the
punctured unit disc into a locally Hermitian symmetric space with
finite volume, the image of the loop around the puncture is a
quasi-unipotent element. This may be viewed as an extension of the
big Picard Theorem to the case of locally Hermitian symmetric
varieties.