The proposed relations for the coefficient ring of the 2-typization of the universal Abel formal group law

Let FAb\mathcal{F}_{Ab} be the universal Abel formal group law, and let its 22-typization have coefficient ring presented as a quotient of the localized Brown–Peterson coefficient ring BP=Z(2)[v1,v2,]BP_* = \mathbb{Z}_{(2)}[v_1,v_2,\ldots]. Write RR for the ideal of relations and let vi=2(2i1)|v_i|=2(2^i-1). For indices 1i<j1\leq i<j and 1i<j1\leq i'<j', let PP denote a monomial not divisible by any v1vi2vj2v_1v_{i'}^2v_{j'}^2. The proposed relations. The coefficient ring is isomorphic to

Λ=Z(2)[v1,v2,]/R,\Lambda=\mathbb{Z}_{(2)}[v_1,v_2,\ldots]/R,

and all generating relations have the form

v1vi2vj2P,1i<j.v_1v_i^2v_j^2\sim P,\qquad 1\leq i<j.

These relations are motivated by explicit low-degree computations of the kernel of the classifying map for the 22-typized Abel formal group law; the parser supplies no evidence that the proposed presentation has been proved or disproved, so its status remains open.

Sources & referencesView supporting material

Primary source

Malkhaz Bakuradze and Mamuka Jibladze, “Some explicit expressions concerning formal group laws”, arXiv:1310.0783 (2014).

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