TY - JOUR
T1 - Building modules from the singular locus
AU - Burke, Jesse
AU - Christensen, Lars Winther
AU - Takahashi, Ryo
PY - 2015
Y1 - 2015
N2 - A finitely generated module over a commutative noetherian ring of finite Krull dimension can be built from the prime ideals in the singular locus by iteration of three procedures: taking extensions, direct summands, and cosyzygies. In 2003 Schoutens gave a bound on the number of iterations required to build any module, and in this note we determine the exact number. This building process yields a stratification of the module category, which we study in detail for local rings that have an isolated singularity.
AB - A finitely generated module over a commutative noetherian ring of finite Krull dimension can be built from the prime ideals in the singular locus by iteration of three procedures: taking extensions, direct summands, and cosyzygies. In 2003 Schoutens gave a bound on the number of iterations required to build any module, and in this note we determine the exact number. This building process yields a stratification of the module category, which we study in detail for local rings that have an isolated singularity.
UR - http://www.scopus.com/inward/record.url?scp=84924273492&partnerID=8YFLogxK
U2 - 10.7146/math.scand.a-20449
DO - 10.7146/math.scand.a-20449
M3 - Article
AN - SCOPUS:84924273492
SN - 0025-5521
VL - 116
SP - 23
EP - 33
JO - Mathematica Scandinavica
JF - Mathematica Scandinavica
IS - 1
ER -