Lemma 4.3 (0MUS) · ScalingStacks

Lemma 4.3. Under the assumptions of Proposition 3.6 we have that

\textnormal{Hom}(S,\Sigma^{i}\mu):\textnormal{Hom}(S,\Sigma^{i}M)\rightarrow% \textnormal{Hom}(S,\Sigma^{i}\bar{M})

is an isomorphism for $i<1$ .

0MUT

Proof: In Lemma 3.3, $\textnormal{Hom}(S,\Sigma^{i}\mu):\textnormal{Hom}(S,\Sigma^{i}M_{k})% \rightarrow\textnormal{Hom}(S,\Sigma^{i}M_{k+1})$ is an isomorphism for $i<1$ . Now apply Lemma 4.2. $\Box$

David Pauksztello

Original source: arXiv:0705.0102v2