Peng Zhou

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blog:2024-12-20 [2024/12/21 08:10] – pzhoublog:2024-12-20 [2024/12/21 08:28] (current) – pzhou
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 One guess is that, the space is still and always is $BGL_k$, and the T-brane sheaf is still $BB \to BG$ pushing forward. But this is like after doing stop removal. How to remember?  One guess is that, the space is still and always is $BGL_k$, and the T-brane sheaf is still $BB \to BG$ pushing forward. But this is like after doing stop removal. How to remember? 
  
 +Another way of thinking is, we don't have to use $[pt/GL_k]$, but $[(pt \to pt)/GL_k]$, and then do sheaves on it. What does it mean? A sheaf of vector spaces on a space $X$, is a functor from the open category to $dgVect$. A sheaf on a quotient stack $[X/G]$, or the category of sheaves on $[X/G]$ is the limit (equalizer in the infinite version)
 +$$ Sh(X) \to Sh(X \times G) \to Sh(X \times G \times G) \to \cdots $$
  
 +
 +But what is $Sh(pt \to pt)$? 
  
  
  
  
blog/2024-12-20.1734768627.txt.gz · Last modified: 2024/12/21 08:10 by pzhou