Shapes of free resolutions over a local ring

Free Resolutions of Lex-ideals over a Koszul Toric Ring

In this paper, we study the minimal free resolution of lex-ideals over a Koszul toric ring. In particular, we study in which toric ring R all lexideals are componentwise linear. We give a certain necessity and sufficiency condition for this property, and show that lex-ideals in a strongly Koszul toric ring are componentwise linear. In addition, it is shown that, in the toric ring arising from t...

Rigid Resolution of a Finitely Generated Module Over a Regular Local Ring

MINIMAL FREE RESOLUTIONS over COMPLETE INTERSECTIONS

We begin the chapter with some history of the results that form the background of this book. We then define higher matrix factorizations, our main focus. While classical matrix factorizations were factorizations of a single element, higher matrix factorizations deal directly with sequences of elements. In section 1.3, we outline our main results. Throughout the book, we use the notation introdu...

2 00 9 Exact Zero Divisors and Free Resolutions over Short Local Rings

Let R be a local ring with maximal ideal m such that there exists a pair of elements a, b with (0 : a) = bR and (0 : b) = aR; we say that a pair a, b as above is an exact pair of zero divisors. We study minimal free resolutions of finitely generated R-modules M , with particular attention to the case when m = 0. Let e denote the minimal number of generators of m. If R is Gorenstein with m = 0 a...

rigid resolution of a finitely generated module over a regular local ring