On the convergence of the orthogonal spectral sequence

2021/11/05 by César Galíndo, Galindo, Cesar, Pablo Pelaez +1 · 1 citation
Mathematics · #14C25 #14C35 #14F42 #19E15 (Primary) 18G55 #55P42 (Secondary) #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2111.03508

openalex publication_date 2021/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the orthogonal spectral sequence introduced by the second author is strongly convergent in Voevodsky's triangulated category of motives DM over a field k. In the context of the Morel-Voevodsky motivic stable homotopy category we provide concrete examples where the spectral sequence is not strongly convergent, and give a criterion under which the strong convergence still holds. This criterion holds for Voevodsky's slices, and as a consequence we obtain a spectral sequence which converges strongly to the E1-term of Voevodsky's slice spectral sequence.

Cited by

• Regular homomorphisms and mixed motives

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