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<p>We present two geometrizations for the group of <i>p</i>-adic characters of the additive group of the ring <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathbb {Z}_{p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Z</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> of <i>p</i>-adic integers. The first geometrization is realized via certain étale sheaves on the Witt ring scheme. The second is constructed in terms of certain quasi-coherent sheaves, equipped with an additional structure, on the formal completion of the Witt ring scheme along its special fiber.</p>

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Geometrization of p-adic characters of \(\mathbb {Z}_{p}\)

  • 期刊论文

  • 发表日期：

    2026年4月15日

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  • Yufan Luo

摘要

We present two geometrizations for the group of p-adic characters of the additive group of the ring \(\mathbb {Z}_{p}\) Z p of p-adic integers. The first geometrization is realized via certain étale sheaves on the Witt ring scheme. The second is constructed in terms of certain quasi-coherent sheaves, equipped with an additional structure, on the formal completion of the Witt ring scheme along its special fiber.