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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 …
Nitin Nitsure's user avatar
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.
Nitin Nitsure's user avatar