论文标题
加权同源规律
Weighted homological regularities
论文作者
论文摘要
令$ a $为noetherian连接的分级代数。我们介绍和研究同源不变量，这些不变性是分级$ a $模型的Cochain复合物的同源和内部程度的加权总和，提供了Castelnuovo的加权版本 - 穆姆福德（Mumford）的加权版本 - 穆姆福德（Mumford）的规律性，tor-regularity，artin-schelter-schelter的规律性和浓汤。在某些情况下，无限的不变（例如Tor-groundity）可以用有限的加权不变式代替，并且复合物的几种同源不变剂可以表示为加权同源规律。我们证明了一些加权的同源性身份，其中一些统一了不同的经典同源性身份并产生有趣的新型。
Let $A$ be a noetherian connected graded algebra. We introduce and study homological invariants that are weighted sums of the homological and internal degrees of cochain complexes of graded $A$-modules, providing weighted versions of Castelnuovo--Mumford regularity, Tor-regularity, Artin--Schelter regularity, and concavity. In some cases an invariant (such as Tor-regularity) that is infinite can be replaced with a weighted invariant that is finite, and several homological invariants of complexes can be expressed as weighted homological regularities. We prove a few weighted homological identities some of which unify different classical homological identities and produce interesting new ones.
