Uniform Artin-Rees bounds for syzygies

作者：Aberbach Ian M; Hosry Aline; Striuli Janet^*

来源：Advances in Mathematics, 2015, 285: 478-496.

DOI：10.1016/j.aim.2015.07.031

• Uniform Artin-Rees
• Free resolutions
• Syzygics
• Complex of standard rank and height
• Koszul complex
• Homology annihilator

Let (R,m) be a local Noetherian ring, let M be a finitely generated R -module and let (F-center dot, partial derivative(center dot)) be a free resolution of M. We find a uniform bound h such that the ArtinRees containment (IFi)-F-n boolean AND I-m partial derivative(i+1) subset of I(n-h)Im partial derivative(i+1) holds for all integers i >= d, for all integers n >= h, and for all ideals I of R. In fact, we show that a considerably stronger statement holds. The uniform bound h holds for all ideals and all resolutions of dth syzygy modules. In order to prove our statements, we introduce the concept of Koszul annihilating sequences.

• 出版日期2015-11-5