منابع مشابه
Infinite Graded Free Resolutions
The idea of associating a free resolution to a finitely generated module was introduced in two famous papers by Hilbert in 1890 [Hi1] and 1893 [Hi2]. He proved Hilbert’s Syzygy Theorem 4.9, which says that the minimal free resolution of every finitely generated graded module over a polynomial ring is finite. Since then, there has been a lot of progress on the structure and properties of finite ...
متن کاملComparison Maps for Relatively Free Resolutions
Let Λ be a commutative ring, A an augmented differential graded algebra over Λ (briefly, DGA-algebra) and X be a relatively free resolution of Λ over A. The standard bar resolution of Λ over A, denoted by B(A), provides an example of a resolution of this kind. The comparison theorem gives inductive formulae f :B(A) → X and g:X → B(A) termed comparison maps. In case that fg = 1X and A is connect...
متن کاملStrategies for Computing Minimal Free Resolutions
One of the most important computations in algebraic geometry or commutative algebra that a computer algebra system should provide is the computation of finite free resolutions of ideals and modules. Resolutions are used as an aid to understand the subtle nature of modules and are also a basis of further computations, such as computing sheaf cohomology, local cohomology, Ext, Tor, etc. Modern me...
متن کاملFree Resolutions and Sparse Determinantal Ideals
A sparse generic matrix is a matrix whose entries are distinct variables and zeros. Such matrices were studied by Giusti and Merle who computed some invariants of their ideals of maximal minors. In this paper we extend these results by computing a minimal free resolution for all such sparse determinantal ideals. We do so by introducing a technique for pruning minimal free resolutions when a sub...
متن کاملPeriodic free resolutions from twisted matrix factorizations
Article history: Received 31 May 2015 Available online 1 March 2016 Communicated by Luchezar L. Avramov MSC: primary 16E05, 16E35, 16E65
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2013
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x12000760