Ragnar-Olaf Buchweitz

TL;DR: In this paper, the authors present a generalization of matrix factorizations to matrix factorization on A~ and D. The results show that the matrix factorisation on D can be expressed as a matrix decomposition of a periodic complex.

TL;DR: In this paper, the authors developed geometric methods for the study of finite modules over a local complete intersection R. They showed that the least number of equations needed to cut out R from a regular local ring equals the codimension of R, where codim R = νR(m)− dim R and m denotes the minimal number of generators of an R-module M.

TL;DR: In this article, it was shown that the Loewy length of the homology modules of a finite free complex F over a local ring R is bounded below by a number depending only on R. This result uncovers, in the structure of modules of finite projective dimension, obstructions to realizing R as a closed fiber of some flat local homomorphism.

TL;DR: In this paper, the authors give a negative answer to the question: if the n-th Hochschild cohomology group of a finite-dimensional algebra over a field vanishes for all sufficiently large n, is the global dimension of the Hochmoor group finite?