Indecomposables with smaller cohomological length in the derived category of gentle algebras
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DOI: 10.1007/s11425-017-9270-x
Abstract: Bongartz (2013) and Ringel (2011) proved that there is no gaps in the sequence of lengths of indecomposable modules for the finite-dimensional algebras over algebraically closed fields. The present paper mainly studies this "no gaps"… read more here.
Keywords: length; cohomological length; derived category; smaller cohomological ... See more keywords
Admissible subcategories in derived categories of moduli of vector bundles on curves
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DOI: 10.1016/j.aim.2019.05.019
Abstract: We show that the Poincar\'e bundle gives a fully faithful embedding from the derived category of a curve of sufficiently high genus into the derived category of its moduli space of bundles of rank $r$… read more here.
Keywords: derived category; admissible subcategories; categories moduli; moduli vector ... See more keywords
On the graded dual numbers, arcs, and non-crossing partitions of the integers
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DOI: 10.1016/j.jalgebra.2018.08.023
Abstract: We give a combinatorial model for the bounded derived category of graded modules over the dual numbers in terms of arcs on the integer line with a point at infinity. Using this model we describe… read more here.
Keywords: graded dual; derived category; crossing partitions; non crossing ... See more keywords
Enhancing the filtered derived category
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DOI: 10.1016/j.jpaa.2018.01.004
Abstract: Abstract The filtered derived category of an abelian category has played a useful role in subjects including geometric representation theory, mixed Hodge modules, and the theory of motives. We develop a natural generalization using current… read more here.
Keywords: category; filtered derived; derived category; enhancing filtered ... See more keywords