Derived categories of coherent sheaves on some zero-dimensional schemes

Alexey Elagin; Valery A. Lunts

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arXiv · 2002.06416

Derived categories of coherent sheaves on some zero-dimensional schemes

Alexey Elagin·Valery A. Lunts

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Abstract

Let $X_N$ be the second infinitesimal neighborhood of a closed point in $N$-dimensional affine space. In this note we study $D^b(coh\, X_N)$, the bounded derived category of coherent sheaves on $X_N$. We show that for $N\geq 2$ the lattice of triangulated subcategories in $D^b(coh\, X_N)$ has a rich structure (which is probably wild), in contrast to the case of zero-dimensional complete intersections. We also establish a relation between triangulated subcategories in $D^b(coh\, X_N)$ and universal localizations of a free graded associative algebra in $N$ variables. Our homological methods produce some applications to the structure of such universal localizations.

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BibTeX RIS

Alexey Elagin, Valery A. Lunts. 2020-02-15. Derived categories of coherent sheaves on some zero-dimensional schemes. https://arxiv.org/abs/2002.06416

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