ﻻ يوجد ملخص باللغة العربية
Numerical invariants of a minimal free resolution of a module $M$ over a regular local ring $(R, )$ can be studied by taking advantage of the rich literature on the graded case. The key is to fix suitable $ $-stable filtrations ${mathbb M} $ of $M $ and to compare the Betti numbers of $M$ with those of the associated graded module $ gr_{mathbb M}(M). $ This approach has the advantage that the same module $M$ can be detected by using different filtrations on it. It provides interesting upper bounds for the Betti numbers and we study the modules for which the extremal values are attained. Among others, the Koszul modules have this behavior. As a consequence of the main result, we extend some results by Aramova, Conca, Herzog and Hibi on the rigidity of the resolution of standard graded algebras to the local setting.
Let fa be an ideal of a local ring (R,fm) and M a finitely generated R-module. This paper concerns the notion fgrade(fa,M), the formal grade of M with respect to fa (i.e. the least integer i such that {vpl}_nH^i_{fm}(M/fa^n M) eq 0). We show that fgr
Let $R$ be a commutative Noetherian ring that is a smooth $mathbb Z$-algebra. For each ideal $I$ of $R$ and integer $k$, we prove that the local cohomology module $H^k_I(R)$ has finitely many associated prime ideals. This settles a crucial outstandin
In a paper in 1962, Golod proved that the Betti sequence of the residue field of a local ring attains an upper bound given by Serre if and only if the homology algebra of the Koszul complex of the ring has trivial multiplications and trivial Massey o
Mustac{t}u{a} has given a conjecture for the graded Betti numbers in the minimal free resolution of the ideal of a general set of points on an irreducible projective algebraic variety. For surfaces in $mathbb P^3$ this conjecture has been proven for
We introduce a new class of arrangements of hyperplanes, called (strictly) plus-one generated arrangements, from algebraic point of view. Plus-one generatedness is close to freeness, i.e., plus-one generated arrangements have their logarithmic deriva