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Ext and the motivic Steenrod algebra over $$\mathbb R$$. (English) Zbl 1222.55014
The author presents some computations of Ext over the dual mod 2 motivic Steenrod algebra $${\mathcal A}$$, or rather its sub-Hopf algebras $$E(n)$$ and $${\mathcal A}(1)$$, over $${\mathbb R}$$, as a preamble to future work of computing motivic stable homotopy groups using the Adams spectral sequence over $${\mathbb R}$$. The method is through a descent style, Bockstein spectral sequence to utilize some corresponding results over $${\mathbb C}$$. The calculations are very delicate.
At the end, the author relates such motivic calculations to the classical ones related to $${\mathbb Z}/2$$-equivariant homotopy, $$BP\langle n\rangle$$, and $$ko$$.

##### MSC:
 55T15 Adams spectral sequences 14F42 Motivic cohomology; motivic homotopy theory
##### Keywords:
Ext; motivic Steenrod algebra; Bockstein spectral sequence
Full Text:
##### References:
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