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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
7
votes
The definition of generalised vector bundles over a scheme : dualise or not?
Here is a place where not dualizing is the right thing to do.
Let $X\to S$
be a projective morphism over a noetherian base $S$, and let $F$ be
a coherent sheaf of ${\mathcal O}_X$-modules
on $X$ that …
6
votes
Accepted
Algebraic spaces as functors on complete local rings
There is an exponential map from complex line to itself. This is not algebraic, but it is defined on complete local ring valued points. So the functor does not appear to be full.