Eventually Linear Partially Complete Resolutions Over a Local Ring with m4=0
School of Science
Journal of Algebra and its Applications
We classify the Hilbert polynomial of a local ring (R,m)(R,𝔪) satisfying m4=0𝔪4=0 which admits a doubly-infinite eventually linear resolution CC which is “partially” complete — that is, for which HiHomR(C,R)HiHomR(C,R) vanishes for all |i|≫0|i|≫0. As a corollary to our main result, we show that an m4=0𝔪4=0 local ring can admit certain classes of asymmetric partially complete resolutions only if its Hilbert polynomial is symmetric. Moreover, we show that the Betti sequence associated to an eventually linear partially complete resolution over an m4=0𝔪4=0 local ring cannot be periodic of period two or three.
Linear resolution, complete resolution, totally reflexive module, Hilbert series
Kristen Beck (Mathematics and Computer Science): “Eventually linear partially complete resolutions over a local ring with m4=0,” Kristen A. Beck, in the Journal of Algebra and its Applications, Vol. 15, No. 03, April 2016. Doi:10.1142/S0219498816500559. http://www.worldscientific.com/doi/abs/10.1142/S0219498816500559
Beck, Kristen. Eventually Linear Partially Complete Resolutions Over a Local Ring with m4=0 (2016). Journal of Algebra and its Applications. 15 (3), 10.1142/S0219498816500559 [article]. https://digitalcommons.stmarys-ca.edu/school-science-faculty-works/7