On the injectivity of certain homomorphisms between extensions of G^(λ) by \mathbbG_m over a ℤ_(p)-algebra

2024/05/18 by Michio Amano, Amano, Michio
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2405.11278

openalex publication_date 2024/05/18 · openalex created_date 2024/05/22 · openalex updated_date 2026/07/28

Abstract

Let \widehatG^(λ) be a formal group scheme which deforms \widehat\mathbbG_a to \widehat\mathbbG_m. And let ψ^(l):\widehatG^(λ)→\widehatG^(λ^pl) be the l-th Frobenius-type homomorphism determined by λ. We show that the homomorphism (ψ^(l))^∗:H²₀(\widehatG^(λ^pl),\widehat\mathbbG_m)→ H²₀(\widehatG^(λ),\widehat\mathbbG_m) induced by ψ^(l) is injective over a ℤ_(p)-algebra under a suitable restriction on λ. In this situation, the Cartier dual of Ker(ψ^(l)), which is a finite group scheme of order p^l, is described over a ℤ/(pⁿ)-algebra.

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