Report
Homologically smooth connected cochain DGAs
| العنوان: | Homologically smooth connected cochain DGAs |
|---|---|
| المؤلفون: | Mao, X. -F. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Rings and Algebras, 16E10, 16E45, 16W50, 16E65 |
| الوصف: | Let $\mathscr{A}$ be a connected cochain DG algebra such that $H(\mathscr{A})$ is a Noetherian graded algebra. We give some criteria for $\mathscr{A}$ to be homologically smooth in terms of the singularity category, the cone length of the canonical module $k$ and the global dimension of $\mathscr{A}$. For any cohomologically finite DG $\mathscr{A}$-module $M$, we show that it is compact when $\mathscr{A}$ is homologically smooth. If $\mathscr{A}$ is in addition Gorenstein, we get $$\mathrm{CMreg}M = \mathrm{depth}_{\mathscr{A}}\mathscr{A} + \mathrm{Ext.reg}\, M<\infty,$$ where $\mathrm{CMreg}M$ is the Castelnuovo-Mumford regularity of $M$, $\mathrm{depth}_{\mathscr{A}}\mathscr{A}$ is the depth of $\mathscr{A}$ and $ \mathrm{Ext.reg}\, M$ is the Ext-regularity of $M$. Comment: arXiv admin note: substantial text overlap with arXiv:1301.4382 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.14803 |
| رقم الانضمام: | edsarx.2407.14803 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |