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I am studying the construction of derived Quot schemes in the paper Borisov, Katzarkov, and Sheshmani - “Shifted symplectic structures on derived Quot-stacks”. Derived quot stacks are constructed from ...

Let $A$ be a dg algebra, and $x, z \in A$ cocycles. Let's consider the maps $$ A \to A \oplus A \to A$$ given by $y \mapsto (xy,yz)$ and $(u,v) \mapsto uz-xv$, respectively. We think of this as ...

Recall that a finite dimensional associative algebra $A$ over a field $k$ is called a symmetric Frobenius algebra (sometimes called "closed" Frobenius algebra) if its equipped with a symmetric non ...

For simplicity let me work only with connected and simply connected spaces. "Space" will mean a space of this type. A space is rational if its homotopy groups are rational vector spaces (...