منابع مشابه
The Motivic Spectral Sequence
In this chapter we explain the Atiyah-Hirzebruch spectral sequence that relates topological K-theory to singular cohomology and try to motivate the search for a motivic version. In the time since [18] appeared, which concerns motivation for such a motivic spectral sequence, many authors have produced results in this direction. We describe the Bloch-Lichtenbaum spectral sequence [8] for the spec...
متن کاملThe Motivic Adams Spectral Sequence
We present some data on the cohomology of the motivic Steenrod algebra over an algebraically closed field of characteristic 0. Our results are based on computer calculations and a motivic version of the May spectral sequence. We discuss features of the associated Adams spectral sequence, and use these tools to give new proofs of some results in classical algebraic topology. We also consider a m...
متن کاملA Spectral Sequence for Motivic Cohomology
We show that, assuming a rather innocuous looking ”moving lemma” called Theorem A, this complex is an exact couple, and the resulting spectral sequence has the form (0.1.1). §2 §6 of the paper are devoted to proving theorem A. Finally, in §7, we prove that t≥1(Z (Spec(F ), )[−4]), the higher Chow complex shifted to the right 4 steps and then truncated so the resulting complex is supported in de...
متن کاملA possible new approach to the motivic spectral sequence for algebraic K-theory
Despite the considerable progress in motivic cohomology and motivic homotopy theory achieved in recent years we still do not have a simple construction of the spectral sequence relating motivic cohomology and algebraic K-theory. The construction invented by Dan Grayson (see [3]) is simple and elegant but we are still unable to identify the E2-term of the resulting spectral sequence with the mot...
متن کاملOn the slice spectral sequence
We introduce a variant of the slice spectral sequence which uses only regular slice cells, and state the precise relationship between the two spectral sequences. We analyze how the slice filtration of an equivariant spectrum that is concentrated over a normal subgroup is related to the slice filtration of its geometric fixed points, and use this to prove a conjecture of Hill on the slice filtra...
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ژورنال
عنوان ژورنال: Journal of the Institute of Mathematics of Jussieu
سال: 2015
ISSN: 1474-7480,1475-3030
DOI: 10.1017/s1474748015000419