Derived categories of coherent sheaves on some zero-dimensional schemes
| Autor: | Valery A. Lunts, Alexey Elagin |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Polynomial
Derived category Algebra and Number Theory Mathematics::Commutative Algebra Zero (complex analysis) Lattice (group) Structure (category theory) Coherent sheaf Combinatorics Mathematics - Algebraic Geometry Mathematics::Category Theory Associative algebra FOS: Mathematics Affine space 14F05 (Primary) 16S10 16S85 (Secondary) Algebraic Geometry (math.AG) Mathematics |
| Popis: | 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. 32 pages, comments are welcome. v2: organization of the paper is changed, minor changes to the text, some reference added |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|