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Homological Algebra for Persistence Modules

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0 Published in 2021 at "Foundations of Computational Mathematics"

DOI: 10.1007/s10208-020-09482-9

Abstract: We develop some aspects of the homological algebra of persistence modules, in both the one-parameter and multi-parameter settings, considered as either sheaves or graded modules. The two theories are different. We consider the graded module… read more here.

Keywords: algebra persistence; persistence modules; homological algebra; persistence ... See more keywords

Duality and de Rham cohomology for graded D-modules

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1 Published in 2018 at "Advances in Mathematics"

DOI: 10.1016/j.aim.2018.07.005

Abstract: We consider the (graded) Matlis dual $\DD(M)$ of a graded $\D$-module $M$ over the polynomial ring $R = k[x_1, \ldots, x_n]$ ($k$ is a field of characteristic zero), and show that it can be given… read more here.

Keywords: duality rham; module; rham cohomology; cohomology ... See more keywords

The associated graded module of the test module filtration

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1 Published in 2017 at "Communications in Algebra"

DOI: 10.1080/00927872.2021.1882475

Abstract: Abstract We show that each direct summand of the associated graded module of the test module filtration admits a natural Cartier structure. If λ is an F-jumping number, then this Cartier structure is nilpotent on… read more here.

Keywords: associated graded; module; test module; module filtration ... See more keywords