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Reflecting Perfection for Finite Dimensional Differential Graded Algebras
Published 4 Oct 2023 in math.KT, math.AG, and math.RT | (2310.02833v2)
Abstract: We generalise two facts about finite dimensional algebras to finite dimensional differential graded algebras. The first is the Nakayama Lemma and the second is that the simples can detect finite projective dimension. We prove two dual versions which relate to Gorenstein differential graded algebras and Koszul duality respectively. As an application, we prove a corepresentability result for finite dimensional differential graded algebras.
- Generators and representability of functors in commutative and noncommutative geometry. Moscow Mathematical Journal, 3:1:36, 05 2002.
- Alexey Bondal and MÂ Kapranov. Representable functors, serre functors, and mutations. Mathematics of the USSR-Izvestiya, 35:519, 10 1989.
- Alexander Efimov. Categorical smooth compactifications and generalized hodge-to-de rham degeneration. Invent. math. 222, 667–694 (2020)., 3, 05 2020.
- Haibo Jin. Cohen-macaulay differential graded modules and negative calabi-yau configurations. Advances in Mathematics, 374:107338, 2020.
- Bernhard Keller. On differential graded categories. arXiv: 0601185, 2006.
- Homologically finite-dimensional objects in triangulated categories. arXiv: 2211.09418, 2022.
- Alexander Kuznetsov. Hochschild homology and semiorthogonal decompositions. arXiv: 0904.4330, 2009.
- N Markarian. Poincaré-Birkoff-Witt isomorphism, Hochshild homology and Riemann-Roch theorem. preprint, 2001.
- Nikita Markarian. The atiyah class, hochschild cohomology and the riemann-roch theorem. Journal of the London Mathematical Society, 79(1):129–143, October 2008.
- Dmitri Orlov. Finite-dimensional differential graded algebras and their geometric realizations. Advances in Mathematics, 366:107096, jun 2020.
- Dmitri Orlov. Smooth dg algebras and twisted tensor product. arXiv: 2305.19799, 2023.
- Proper connective differential graded algebras and their geometric realizations. arXiv: 1903.02849, 2020.
- D. Shklyarov. On serre duality for compact homologically smooth dg algebras. arXiv: 0702590, 2007.
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