Ravenel's Global Conjecture for formal module Ext groups, precise form

Let K/QK/\mathbb{Q} be a finite Galois extension with ring of integers AA. An ideal II of AA is nn-congruing if, for every aAa\in A, there exists NNN\in\mathbb{N} such that aN(an1)Ia^N(a^n-1)\in I; let JnJ_n be the minimal nn-congruing ideal. For some cNc\in\mathbb{N} and every nNn\in\mathbb{N}, Ravenel's Global Conjecture.

Ext(LA,LAB)1,2n(LA,LA)[c1]A/(Jn)[c1].\operatorname{Ext}_{(L^A,L^AB)}^{1,2n}(L^A,L^A)[c^{-1}] \cong A/(J_n)[c^{-1}].

The localization by a correcting integer captures the small factor left unspecified in Ravenel's original formulation. The paper presents this as a rigorous version of the global conjecture, after proving existence and uniqueness of the minimal nn-congruing ideal; the general assertion remains open in the supplied text.

Sources & referencesView supporting material

Primary source

A. Salch, “Ravenel's Global Conjecture is true”, arXiv:1511.05288 (2015).

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