Higher semiadditive Grothendieck-Witt theory and the 𝐾(1)-local sphere

Communications of the American Mathematical Society Pub Date : 2021-09-24 DOI:10.1090/cams/17

Shachar Carmeli, Allen Yuan

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引用次数: 5

Abstract

We develop a higher semiadditive version of Grothendieck-Witt theory. We then apply the theory in the case of a finite field to study the higher semiadditive structure of the K ( 1 ) K(1) -local sphere S K ( 1 ) \mathbb {S}_{K(1)} at the prime 2 2 , in particular realizing the non- 2 2 -adic rational element 1 + ε ∈ π 0 S K ( 1 ) 1+\varepsilon \in \pi _0\mathbb {S}_{K(1)} as a “semiadditive cardinality.” As a further application, we compute and clarify certain power operations in π 0 S K ( 1 ) \pi _0\mathbb {S}_{K(1)} .

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高半加性Grothendieck-Witt理论与𝐾(1)局部球

我们发展了Grothendieck-Witt理论的高半加性版本。然后，我们将该理论应用于有限域的情况下，研究了K(1) K(1) -局部球S K(1) \mathbb S＿K{(1)在素数22处}的高半加性结构。特别是实现了非- 2 2进有理数元素1+ ε∈π 0 S K(1) 1+ {}\varepsilon\in\pi ＿0 \mathbb S＿K{(}1)作为{“半加性的cardinality”。作为进一步的应用，我们计算并阐明了π 0 S＿K(1) }\pi ＿0 \mathbb S＿K{(}1)中的一些幂运算。{}

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Communications of the American Mathematical Society

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