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On the derived category of the classical Godeaux surface
the derived category the classical Godeaux surface Algebraic Geometry
2012/6/30
We construct an exceptional sequence of length 11 on the classical Godeaux surface X which is the Z/5-quotient of the Fermat quintic surface in P^3. This is the maximal possible length of such a seque...
Not every object in the derived category of a ring is Bousfield equivalent to a module
Not every object derived category ring Bousfield equivalent module
2012/3/1
We consider the derived category of a specific non-Noetherian ring \Lambda, and show that there are objects in D(\Lambda) that are not Bousfield equivalent to any module. This answers a question posed...
On the derived category of a graded commutative noetherian ring
Localizing subcategories graded ring weighted projective scheme
2011/9/20
Abstract: For any graded commutative noetherian ring, where the grading group is abelian and where commutativity is allowed to hold in a quite general sense, we establish an inclusion-preserving bijec...
Scheme of lines on a family of 2-dimensional quadrics: geometry and derived category
2-dimensional quadrics geometry derived category
2010/11/23
Given a generic family $Q$ of 2-dimensional quadrics over a smooth 3-dimensional base $Y$ we consider the relative Fano scheme $M$ of lines of it. The scheme $M$ has a structure of a generically coni...
Equivalence of the Derived Category of a Variety with a Singularity Category
Variety Singularity Category
2010/11/11
We prove an equivalence between the derived category of a variety and the equivariant/graded singularity category of a corresponding singular variety. The equivalence also holds at the dg level.
We consider the category of Deligne 1-motives over a perfect field k of exponential characteristic p and its derived category for a suitable exact structure after inverting p.