合成上同调与THH中的科尔曼同构
Coleman Isomorphisms in Syntomic Cohomology and $\mathrm{THH}$
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中文总结 AI 辅助
本文将科尔曼同构推广到多种上同调理论，通过分圆合成谱描述THH分圆塔的传递映射极限，构造了相关传递映射，为伊瓦萨理论应用奠定基础。
中文摘要 AI 辅助
本文证明了科尔曼同构（范数相容分圆单位与可逆幂级数群之间的同构）在定义于真正则p进形式概型上的多种上同调理论中的推广，以供后续在伊瓦萨理论中的应用。该推广是对动机过滤THH的分圆塔上传递映射极限的分圆合成谱描述的直接结果。这一过程关键使用了Devalapurkar-Raksit关于THH(ℤₚ[ζₚⁿ])的计算，以及Schlichtkrull关于自由环传递的计算。在此过程中，我们利用P¹-稳定动机同伦理论的一些元素，构造了有限局部自由正则映射下多种上同调理论的传递映射。
英文摘要
This paper proves a generalisation of Coleman's isomorphism (between norm compatible cyclotomic units and a group of invertible power series) to various cohomology theories evaluated on proper regular $p$-adic formal schemes, for future applications to Iwasawa theory. This generalisation is an immediate consequence of a description, as a cyclotomic synthetic spectrum, of the limit over transfer maps as one goes up the cyclotomic tower of motivically filtered $\mathrm{THH}$. This crucially uses a calculation of $\mathrm{THH}(\mathbb{Z}_p[ζ_{p^n}])$ due to Devalapurkar--Raksit as well as a calculation of the free loop transfer due to Schlichtkrull. Along the way, we construct transfer maps for various cohomology theories along finite locally free regular maps, using some elements of $\mathbb{P}^1$-stable motivic homotopy theory.
