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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
-1
votes
Flat quasi-coherent modules as colimits of locally free ones
This is a local property. [if $M$ comes from an algebra over $A$]. It reduces to consider the case that $X=\text{Spec}(A)$ is an affine scheme.
If the ring $A$ is a PID, I think the statement is true …
-2
votes
Can we define homotopy groups using Tannakian categories
In Quillen's algebraic K-theory, higher homotopy groups are defined in a simplicial manner. It's maybe used to get an algebraic version of higher homotopy groups for some special cases.
Even in such …