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Supports and filtrations in algebraic geometry and modular representation theory
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 129, Number 5, October 2007
- pp. 1227-1250
- 10.1353/ajm.2007.0030
- Article
- Additional Information
Working with tensor triangulated categories, we prove two theorems relative to supports and then discuss their incarnations in algebraic geometry and in modular representation theory. First, we show that an indecomposable object has connected support. Then we consider the filtrations by dimension or codimension of the support and prove that the associated subquotients decompose as sums of local terms.