Hello pricey customer to our community We will proffer you an answer to this query ag.algebraic geometry – Ok/G-theory of affine bundles ,and the respond will breathe typical by way of documented data sources, We welcome you and proffer you fresh questions and solutions, Many customer are questioning concerning the respond to this query.
ag.algebraic geometry – Ok/G-theory of affine bundles
Setting: $f : C to D$ is a morphism of Artin stacks over $X$ which is a torsor for a vector bundle $T to X$: étale-locally in $X$, we have now $C simeq D times_X T$. I need to resolve that $f^*: G(D) to G(C)$ (or the identical for $Ok$-theory) is injective.
Exercise V 6.6 within the $Ok$-book by Ch. Weibel states that for flat maps $E to X$ of noetherian schemes with fibers given by affine house, the pullback is an equivalence on G-theory. The fibers over geometric factors of $f$ are affine house, however it might breathe that many fibers don’t have any sections. Moreover, I need to employ this reality on Artin stacks as an alternative of schemes, defining their G-theory/Ok-theory utilizing websites launched by Olsson in “Sheaves on Artin stacks” as elaborated in Feng Qu’s “Virtual pullbacks in K-theory.”
Thanks for the ameliorate — I’m considerably fresh to Ok-theory.
we’ll proffer you the answer to ag.algebraic geometry – Ok/G-theory of affine bundles query by way of our community which brings all of the solutions from a number of dependable sources.