由模ℓ Milnor K理论重构函数域
Reconstruction of Function Fields from Mod-ℓ Milnor K-Theory
OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。
具体内容
稿件证明模ℓ的Bogomolov–Pop重构定理，适用于特征不等于ℓ的任意代数闭域上超越次数至少二的函数域。作者声称群K^M₁/ℓ与K^M₂/ℓ连同其完整双线性积可决定完美闭包及其常数域；每个相容同构由域同构诱导，至多差F_ℓ^×中一个标量，正特征下域同构仅有Frobenius歧义。当前收录摘要未给出证明，手稿未经独立审查。
- 对超越次数≥2的函数域证明模ℓ Bogomolov–Pop重构。
- K^M₁/ℓ与K^M₂/ℓ及双线性积决定完美闭包与常数域。
- 相容同构由域同构诱导，至多差F_ℓ^×标量与Frobenius歧义。
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英文原始摘要
We prove a mod-ℓ Bogomolov–Pop reconstruction theorem for function fields of transcendence degree at least two over arbitrary algebraically closed fields of characteristic different from ℓ. The groups $`K^{\mathrm M}_1/\ell`$ and $`K^{\mathrm M}_2/\ell`$, together with their full bilinear product, determine the perfect closure and its constant field. Every compatible isomorphism of these data is induced by a field isomorphism up to a single scalar in $`\mathbb F_\ell^\times`$, with only Frobenius ambiguity in the field isomorphism in positive characteristic.
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