The homotopy Leray spectral sequence

Aravind Asok; Frédéric Déglise; Jan Nagel

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arXiv · 1812.09574

The homotopy Leray spectral sequence

Aravind Asok·Frédéric Déglise·Jan Nagel

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Abstract

In this work, we build a spectral sequence in motivic homotopy that is analogous to both the Serre spectral sequence in algebraic topology and the Leray spectral sequence in algebraic geometry. Here, we focus on laying the foundations necessary to build the spectral sequence and give a convenient description of its $E_2$-page. Our description of the $E_2$-page is in terms of homology of the local system of fibers, which is given using a theory similar to Rost's cycle modules. We close by providing some sample applications of the spectral sequence and some hints at future work.

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Aravind Asok, Frédéric Déglise, Jan Nagel. 2018-12-22. The homotopy Leray spectral sequence. https://arxiv.org/abs/1812.09574

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