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

5 votes
Accepted

dimension of D^b(coh( P^1))

Let me give a name to notion. If $T$ is a triangulated category and $G$ is an object, the minimal number of cones required to generate any object of $T$ starting with $G$ (and allowing for arbitrary f …
Matthew Ballard's user avatar
9 votes
Accepted

Equivalence of derived categories which is not Fourier-Mukai

Schlichting gave an example of two categories of singularities which are derived equivalent but whose K-groups are not isomorphic. Dugger and Shipley (arXiv:0710.3070) expanded on this example and not …
Matthew Ballard's user avatar
7 votes

Mirror symmetry mod p?! ... Physics mod p?!

To me, it seems that the operation mirror to the changing of the base field is the changing of coefficients in Floer homology. Let me give you some examples. For the case when $k$ is any field, we hav …
Matthew Ballard's user avatar