论文标题
代数K理论和Grothendieck-Witt Monoid方案理论
Algebraic K-theory and Grothendieck-Witt theory of monoid schemes
论文作者
论文摘要
我们研究了代数$ k $ - 理论和格罗伦迪克·奈特的原始载体类别的载体束类别的理论。 Our main results are the complete description of the algebraic $K$-theory space of an integral monoid scheme $X$ in terms of its Picard group $\operatorname{Pic}(X)$ and pointed monoid of regular functions $Γ(X, \mathcal{O}_X)$ and a description of the Grothendieck-Witt space of $X$ in terms of an additional involution on $ \ operatatorName {pic}（x）$。我们还证明了两个设置中的空间级投影束公式。
We study the algebraic $K$-theory and Grothendieck-Witt theory of proto-exact categories of vector bundles over monoid schemes. Our main results are the complete description of the algebraic $K$-theory space of an integral monoid scheme $X$ in terms of its Picard group $\operatorname{Pic}(X)$ and pointed monoid of regular functions $Γ(X, \mathcal{O}_X)$ and a description of the Grothendieck-Witt space of $X$ in terms of an additional involution on $\operatorname{Pic}(X)$. We also prove space-level projective bundle formulae in both settings.
