Two Mayer-Vietoris spectral sequences for $\mathcal{D}$-modules

Alberto Casta\~no Dom\'inguez

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Two Mayer-Vietoris spectral sequences for mathcal{D}-modules

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arxiv 1311.1789 v2 pith:447XZD7W submitted 2013-11-07 math.AG

Two Mayer-Vietoris spectral sequences for $\mathcal{D}$-modules

Alberto Casta\~no Dom\'inguez This is my paper

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keywords closedcomplementmathcalmodulessequencesspectralalgebraalgebraic

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abstract

We provide two Mayer-Vietoris-like spectral sequences related to the localization over the complement of a closed subvariety of an algebraic variety by using techniques from $\mathcal{D}$-modules and homological algebra. We also give, as an application of the previous, a method to calculate the cohomology of the complement of any arrangement of hyperplanes over an algebraically closed field of characteristic zero.

Two Mayer-Vietoris spectral sequences for $\mathcal{D}$-modules

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