Monodromy of subvarieties of PEL-Shimura varieties
The aim of this paper is to generalize results of C.-L. Chai about the monodromy of Hecke invariant subvarieties to Shimura varieties of PEL-type.
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arXiv subjects
Ralf Kasprowitz
Publications and source records attributed to Ralf Kasprowitz.
Semistable vector bundles and Tannaka duality from a computational point of view
We develop a semistability algorithm for vector bundles which are given as a kernel of a surjective morphism between splitting bundles on the projective space over an algebraically closed field K. This class of bundles is a generalization of syzygy bundles. We show how to implement this algorithm in a computer algebra system. Further we give applications, mainly concerning the computation of Tannaka dual groups of stable vector bundles of degree 0 on the projective space and on certain smooth complete intersection curves. We also use our algorithm to close an open case left in a recent work of L. Costa, P. Macias Marques and R. M. Miro-Roig regarding the stability of the syzygy bundle of general forms. Finally, we apply our algorithm to provide a computational approach to tight closure. All algorithms are implemented in the computer algebra system CoCoA.
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Monodromy Groups of Vector Bundles on p-adic Curves
In [DW05] and [DW07], C. Deninger and A. Werner developed a partial p-adic analogue of the classical Narasimhan-Seshadri correspondence between vector bundles and representations of the fundamental group. We will investigate the various monodromy groups that occur in this theory, that is the image of these representations and their Zariski closure as well as the Tannaka dual group of these vector bundles.
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