Theoretical study reveals asymptotic growth formulas in ramified graph extensions, indicating algebraic interpretations of characteristic ideals in graph Iwasawa theory.
In this article, we study questions pertaining to ramified Z p d Zₚᵈ double struck upper Z Subscript p Superscript d -extensions of a finite connected graph X X upper X . Let X ∞ X_∞ upper X Subscript infinity denote a Z p d Zₚᵈ double struck upper Z Subscript p Superscript d ramified derived graph of X X upper X (with d ≥ 1 d≥ 1 d greater than or equals 1 ) and Λ Λ normal upper Lamda denote the associated Iwasawa algebra. We first prove an asymptotic growth formula in this general setting and show that it is possible to interpret the characteristic ideal of Pic Λ ( X ∞ ) PicΛ(X_∞ )
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Kundu et al. (2026) studied this question.
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