All Questions

Katzarkov-Kontsevich-Pantev define a smooth dg ($\mathbb{C}$-)algebra $A$ to be a dg algebra which is a perfect $A \otimes A^{op}$-module. They say that an $A$-module $M$ is perfect if the functor $...

Let $X$ be a complex algebraic variety. The rational cohomology of $X(\mathbb{C})$ carries a canonical filtration called the weight filtration. It also carries a canonical equivalence class of $A_\...

I know how to think about (curved) $A_\infty$-algebras 'geometrically', i.e. via formal non-commutative geometry in the sense of Kontsevich etc. I also know how to think about $A_\infty$-morphisms in ...

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 ...

I currently am studying $A_{\infty}$-obstructions and to compute them I need to compute at least the $A_3$-data of an $\mathrm{Ext}$-algebra. More precisely, I have a functor $F:\mathcal{D}\left(X\...

I am currently trying to control an $A_\infty$-algebra of the form $\mathrm{Ext}_X(F\oplus F'[2n-2],F\oplus F'[2n-2])$ where $X$ is a nice enough scheme and $F,F'$ are sheaves that are NOT locally ...