论文标题
共同支持品种的界限
Bounds on cohomological support varieties
论文作者
论文摘要
在本地环$ r $上，共同体支持品种的理论都附加到有限生成的$ r $ modules的任何有限的复合物$ m $上，一个代数品种$ v_r（m）$，该$ v_r（m）$（m）$ n o $ m $。在$ r $的经典不变性方面，我们给出了$ v_r（m）$的尺寸的下限。特别是，当$ r $是Cohen-Macaulay而不是完整的交叉点时，我们发现总有一些品种无法实现为任何复杂的共同体支持。当$ m $具有有限的投影尺寸时，我们还根据$ r $ $ r $的均值lie代数为$ \ dim v_r（m）$的上限。这导致了由于有限自由综合体长度，由于Avramov，Buchweitz，Iyengar和Miller的界限改善。最后，我们将可能发生的品种完全分类为Golod环上复合物的共同体支持。
Over a local ring $R$, the theory of cohomological support varieties attaches to any bounded complex $M$ of finitely generated $R$-modules an algebraic variety $V_R(M)$ that encodes homological properties of $M$. We give lower bounds for the dimension of $V_R(M)$ in terms of classical invariants of $R$. In particular, when $R$ is Cohen-Macaulay and not complete intersection we find that there are always varieties that cannot be realized as the cohomological support of any complex. When $M$ has finite projective dimension, we also give an upper bound for $ \dim V_R(M)$ in terms of the dimension of the radical of the homotopy Lie algebra of $R$. This leads to an improvement of a bound due to Avramov, Buchweitz, Iyengar, and Miller on the Loewy lengths of finite free complexes. Finally, we completely classify the varieties that can occur as the cohomological support of a complex over a Golod ring.
