Purity of stable pieces in compactifications of semisimple groups

• Applicant: Professor Dr. Torsten Wedhorn
• Subject Area: Mathematics
• Term: from 2009 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 124649447

One of the most fruitful techniques to understand geometric objects is to attach to them linear invariants. The study of these invariants often leads to a problem within representation theory. One important question for these invariants is whether they have the property to be pure. A positive answer allows to control the degeneration of geometric objects. An important linear invariant is the De Rham cohomology. For certain geometric objects playing a central role in number theory (e.g., abelian varieties, curves, or p-divisible groups in positive characteristic) their De Rham cohomology carries the structure of a so-called truncated crystal. These can be considered in two ways as objects within the area of representation theory: as representation of certain clans in the sense of Crawley-Boevey or as stable pieces in a compactification of the projective linear group. The goal of this project is to study whether the De Rham cohomology is pure focussing on the second interpretation.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1388: Representation Theory