Timeline for K-theory of the infinite dimensional projective space

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Dec 20, 2017 at 11:13	comment	added	Jason Starr		The Barth-Van de Ven-Tyurin-Sato theorem implies that $K^0$, the $K$-ring of locally free sheaves on ind-projective space, is the subring $\mathbb{Z}[x,x^{-1}] \subset \mathbb{Q}[c]_{\langle c \rangle}$, where $x$ is the class of $[\mathcal{O}(-1)]$ and $c$ equals $1-x$. The ind-projective space "approximates" the Artin stack $B\mathbb{G}_m$, and the $K$-group of this Artin stack is $\mathbb{Q}[[c]]$, cf. the thesis of Toen. So your guess is plausible. You might check Gaitsgory's work on ind-coherent sheaves.
Dec 20, 2017 at 7:17	comment	added	Mikhail Bondarko		Actually, I am reading a short text of somebody else, and there is no definition included. This should be an ind-variety, and one should be able to apply the Barth-Van de Ven-Tyurin-Sato theorem to it.
Dec 20, 2017 at 7:12	history	edited	Mikhail Bondarko	CC BY-SA 3.0	Does the answer depend on the definition of the infinite dimensional projective space?
Dec 19, 2017 at 22:24	comment	added	Jason Starr		What precisely is your definition of the infinite dimensional projective space over a field?
Dec 19, 2017 at 21:40	history	asked	Mikhail Bondarko	CC BY-SA 3.0