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A Mayer-Vietoris-type spectral sequence

Rafael Holanda
Universidade Federal da Paraìba
Friday, June 10, 2022 - 16:30 to 17:30

In order to investigate the interplay between (multigraded) Castelnuovo-Mumford regularity with respect to certain homogeneous finitely generated ideals, we study Cech cohomology (at both sheaf and ring levels) with respect to products of finitely generated ideals. This leads us to construct a spectral sequence which relates local or sheaf cohomologies supported in different ideals and degenerates in the well-known Mayer-Vietoris long exact sequence. In this talk, we invoke general facts about Cech cohomology, build our spectral sequence, and comment on a possible relation with a Lyubeznik spectral sequence and regularity. It is an ongoing joint work with Marc Chardin (Sorbonne Université) and José Naéliton (UFPB). 

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