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Recent results on quiver sheaves

Andreas Laudin, Alexander Schmitt (2012)

Open Mathematics

In this article, we survey recent work on the construction and geometry of representations of a quiver in the category of coherent sheaves on a projective algebraic manifold. We will also prove new results in the case of the quiver • ← • → •.

Recognizing dualizing complexes

Peter Jørgensen (2003)

Fundamenta Mathematicae

Let A be a noetherian local commutative ring and let M be a suitable complex of A-modules. It is proved that M is a dualizing complex for A if and only if the trivial extension A ⋉ M is a Gorenstein differential graded algebra. As a corollary, A has a dualizing complex if and only if it is a quotient of a Gorenstein local differential graded algebra.

Recollements induced by good (co)silting dg-modules

Rongmin Zhu, Jiaqun Wei (2023)

Czechoslovak Mathematical Journal

Let U be a dg- A -module, B the endomorphism dg-algebra of U . We know that if U is a good silting object, then there exist a dg-algebra C and a recollement among the derived categories 𝐃 ( C , d ) of C , 𝐃 ( B , d ) of B and 𝐃 ( A , d ) of A . We investigate the condition under which the induced dg-algebra C is weak nonpositive. In order to deal with both silting and cosilting dg-modules consistently, the notion of weak silting dg-modules is introduced. Thus, similar results for good cosilting dg-modules are obtained. Finally, some...

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