Alessandro Lehmann

activity

20242026

collaborators

4 papers

math.AG2026

An Orlov theorem for matrix factorizations with multiple factors

Alessandro Lehmann, Nicolò Sibilla

We prove a generalization of Orlov's theorem for matrix factorizations with $n$ steps. Let $X$ be a regular scheme, $W : X \to A^{1}$ a flat morphism and $D := W^{- 1} (0)$ i…

math.AG2025

Hochschild cohomology and extensions of triangulated categories

Alessandro Lehmann, Wendy Lowen

We define a notion of categorical first order deformations for (enhanced) triangulated categories. For a category $T$ , we show that there is a bijection between $\operato…

math.KT2024

Hochschild cohomology parametrizes curved Morita deformations

Alessandro Lehmann

We show that, if one allows for curved deformations, the canonical map introduced in [KL09] between Morita deformations and second Hochschild cohomology of a dg algebra becomes a b…

math.KT2024

Filtered derived categories of curved deformations

Alessandro Lehmann, Wendy Lowen

We propose a solution to the "curvature problem" from arXiv:1505.03698 and arXiv:0905.3845 for infinitesimal deformations. Let $k$ be a field, $A$ a dg algebra over $k$ and $A_n =…