Derived categories of coherent sheaves on some zero-dimensional schemes

2020/02/15 by Elagin, Alexey, Lunts, Valery A.
#14F05 (Primary) 16S10 #16S85 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.06416

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≥ 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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