arXiv subjects

Ernest E. Fontes

Publications and source records attributed to Ernest E. Fontes.

2 recordsLinked to original sources

arXiv2020

A Fundamental Theorem for the $K$-theory of connective $\mathbb{S}$-algebras

Invoking the density argument of Dundas-Goodwillie-McCarthy, we extend the Fundamental Theorem of $K$-theory from the category of simplicial rings to the category of $\mathbb{S}$-algebras. As an intermediate step, we prove the Fundamental Theorem for simplicial rings appealing to recent results from the first author's thesis. This recovers as a special case the Fundamental Theorem for the $K$-theory of spaces appearing in Hüttemann-Klein-Vogell-Waldhausen-Williams.

math.KT↗

arXiv2019

Weight structures and the algebraic $K$-theory of stable $\infty$-categories

We introduce the notion of a bounded weight structure on a stable $\infty$-category and use this to prove the natural generalization of Waldhausen's sphere theorem: We show that the algebraic $K$-theory of a stable $\infty$-category with a bounded non-degenerate weight structure is equivalent to the algebraic $K$-theory of the heart of the weight structure.

math.KT↗