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Niels
Niels
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If $G$ is an affine groupe scheme over some base $S$, you can consider the groupoid $G\rightrightarrows S$. The corresponding prestack $[G\rightrightarrows S]^{pre}$ is (equivalent) to) the prestack of trivial $G$-torsors. The corresponding stack $[G\rightrightarrows S]$ is (equivalent to) the stack of $G$-torsors. So it is right to think of the later as the stackification of the former. You can find details in Laumont and Moret-Bailly's book or in Olsson's book.

If $G$ is an affine groupe scheme over some base $S$, you can consider the groupoid $G\rightrightarrows S$. The corresponding prestack $[G\rightrightarrows S]^{pre}$ is (equivalent) to the prestack of trivial $G$-torsors. The corresponding stack $[G\rightrightarrows S]$ is (equivalent to) the stack of $G$-torsors. So it is right to think of the later as the stackification of the former. You can find details in Laumont and Moret-Bailly's book or in Olsson's book.

If $G$ is an affine groupe scheme over some base $S$, you can consider the groupoid $G\rightrightarrows S$. The corresponding prestack $[G\rightrightarrows S]^{pre}$ is (equivalent to) the prestack of trivial $G$-torsors. The corresponding stack $[G\rightrightarrows S]$ is (equivalent to) the stack of $G$-torsors. So it is right to think of the later as the stackification of the former. You can find details in Laumont and Moret-Bailly's book or in Olsson's book.

Source Link
Niels
Niels
  • 4k
  • 1
  • 20
  • 20

If $G$ is an affine groupe scheme over some base $S$, you can consider the groupoid $G\rightrightarrows S$. The corresponding prestack $[G\rightrightarrows S]^{pre}$ is (equivalent) to the prestack of trivial $G$-torsors. The corresponding stack $[G\rightrightarrows S]$ is (equivalent to) the stack of $G$-torsors. So it is right to think of the later as the stackification of the former. You can find details in Laumont and Moret-Bailly's book or in Olsson's book.