Research
Enhancements of triangulated categories, Noncommutative motives and Grothendieck duality
My research interests concern triangulated categories, dg-categories, A∞-categories and stable ∞-categories. I am also interested in some aspect of noncommutative motives and Grothendieck duality for schemes and algebraic stacks.
Papers & Preprint:
A. Canonaco, M. Ornaghi, and P. Stellari, Localization of the category of A∞-categories and Internal Homs over a ring, https://arxiv.org/abs/2404.06610, 2024, (35 pages).
M. Ornaghi, S. Singh and A. Yekutieli, Rigid Dualizing Complexes and their Functorial Properties, https://arxiv.org/abs/2402.07150 , 2024, (119 pages).
M. Ornaghi, The Homotopy Theory of A∞-categories, 2023, (40 pages).
A. Canonaco, M. Ornaghi, and P. Stellari, Localization of the category of A∞-categories and Internal Homs, Doc. Math. 24, 2019, pp. 2463-2492, DOI: 10.25537/dm.2019v24.2463-2492 .
F. Amodeo, R. Moschetti, M. Ornaghi, Equivalences of derived categories of equivariant sheaves, arXiv:1810.13290 , (19 pages).
M. Ornaghi, L. Pertusi, Voevodsky's conjecture for cubic fourfolds and Gushel-Mukai fourfolds via noncommutative K3 surfaces, J. Noncommut. Geom. Volume 13, Issue 2, 2019, pp. 499–515, DOI:10.4171/JNCG/328.
M. Ornaghi, A comparison between pretriangulated A∞-categories and ∞-categories stable, pdf arXiv:1609.00566 , (22 pages).