Bounds on cohomological support varieties
| Autor: | Briggs, Benjamin, Grifo, Eloísa, Pollitz, Josh |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Trans. Amer. Math. Soc. Ser. B 11 (2024), 703-726 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1090/btran/182 |
| Popis: | 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. Comment: Final version |
| Databáze: | arXiv |
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