Abstract

Numerical invariants of a minimal free resolution of a module over a regular local ring can be studied by taking advantage of the rich literature on the graded case. The key is to fix suitable stable filtrations of the module and to compare its Betti numbers with those of the associated graded module. In this course, we will present several applications for the above idea. In particular, we introduce consecutive cancellation method to compute the Betti numbers of filtered modules.

The workshop includes the following lectures:
1) The introduction of blowup Algebras, filtered modules and related problems.
2) Standard basis of filtered modules.
3) Minimal free resolution of finitely generated modules over a local ring.
4) Consecutive cancellations in the Betti numbers of filtered modules.




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