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Tagged with abstract-nonsense noncommutative-geometry
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Are these two "FUNCTORS" adjoint?
I am considering the following correspondence:
Let $X$ be quasi compact quasi separated schemes.Consider a pseudo functor \begin{equation}Sch\rightarrow CAT :U\mapsto Qcoh(U),f:U\rightarrow V\mapsto f^...
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If the direct image of f preserves coherent sheaves on noetherian schemes, how to show f is proper?
The other direction is well known.
I think it is true and I was told by several other guys doing algebraic geometry that it is indeed true but they did not know how to prove. I am also wondering ...