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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

6 votes
1 answer
2k views

Information and intuition packed in the Chern character for coherent sheaves

even after quite some time learning it, I still get somehow puzzled by the Chern character. Let me recall some stuff to get notation and setting. Let us consider a smooth projective algebraic variety …
mGb's user avatar
  • 155
2 votes
1 answer
937 views

on universal homeomorphisms between schemes

We are taught since when we are young that schemes are cool because they take into account "nilpotents". This means also that we can distinguish between schemes which have the same underlying topologi …
mGb's user avatar
  • 155
5 votes
1 answer
423 views

Twisted derived Morita theory of schemes

It has been proved by Toën and Lunts-Schnürer that the dg category $\mathrm{L}_{qcoh}(X\times Y)$ of quasi-coherent sheaves over the product of two quasi-compact, quasi separated (and flat over a comm …
mGb's user avatar
  • 155
2 votes
0 answers
213 views

Quantities associated to deformed sheaves

I am trying to figure out what happens to "quantities" associated to a sheaf when one deforms it. I am actually interested in deforming a bounded complex of coherent sheaves but I want to make the pic …
mGb's user avatar
  • 155