6533b86dfe1ef96bd12ca9c1
RESEARCH PRODUCT
The homotopy Leray spectral sequence
Jan NagelAravind AsokFrédéric Déglisesubject
Serre spectral sequencePure mathematicsHomotopy[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]K-Theory and Homology (math.KT)Leray spectral sequenceAlgebraic geometryHomology (mathematics)Mathematics::Algebraic TopologyMathematics - Algebraic GeometryLocal systemMathematics::K-Theory and HomologySpectral sequenceMathematics - K-Theory and HomologyFOS: MathematicsMSC 14F42 (14-06)Algebraic Topology (math.AT)Mathematics - Algebraic Topology14F42 55R20 19E15[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]Algebraic Geometry (math.AG)Mathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-12-22 |