The nilpotence theorem for the algebraic K–theory of the sphere spectrum

Blumberg, Andrew¹ ; Mandell, Michael²

¹ Department of Mathematics, University of Texas, Austin, TX, United States
² Department of Mathematics, Indiana University, Bloomington, IN, United States

Geometry & topology, Tome 21 (2017) no. 6, pp. 3453-3466.

Résumé

We prove that in the graded commutative ring $K_{\ast }\left(\mathbb{S}\right)$, all positive degree elements are multiplicatively nilpotent. The analogous statements also hold for ${TC}_{\ast }{\left(\mathbb{S}\right)}_p^{\wedge }$ and $K_{\ast }\left(\mathbb{Z}\right)$.

Détail

DOI : 10.2140/gt.2017.21.3453

Classification : 19D10
Keywords: algebraic $K$–theory of spaces, nilpotence theorem, $p$–adic $L$–function

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