The universal thickening of the eld of real numbers
The universal thickening of the eld of real numbers
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实数领域的普遍增厚
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
C. Consani
中科院分区：
文献类型：
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作者：
A. Connes;C. Consani
我们证明了实数域的泛一维增厚。这一建设分三个步骤进行，这三个步骤平行于普遍完美、威特建设和完成过程。证明了完备过程在实阿基米德空间的移位等同于“反量子化”过程，得到了Viro的热带实超域T_R。然后，我们证明了超域背景下的阿基米德Witt结构允许从超域中恢复一个超域，并得到了R的普适准内积增厚R_1。最后，我们给出了几个用于构造p-进周期环的代数的实类似。
We dene the universal 1-adic thickening of the eld of real numbers. This construction is performed in three steps which parallel the universal perfection, the Witt construction and a completion process. We show that the transposition of the perfection process at the real archimedean place is identical to the \dequantization" process and yields Viro’s tropical real hypereld T R. Then we prove that the archimedean Witt construction in the context of hyperelds allows one to recover a eld from a hypereld, and we obtain the universal pro-innitesimal thickening R1 of R. Finally, we provide the real analogues of several algebras used in the construction of the rings of p-adic periods. We