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for questions about deformation theory, including deformations of manifolds, schemes, Galois representations, and von Neumann algebras.

40 votes
Accepted

Deformation theory and differential graded Lie algebras

I hope to write more on this later, but for now let me make some general assertions: there are general theorems to this effect and give two references: arXiv:math/9812034, DG coalgebras as formal stac …
David Ben-Zvi's user avatar
13 votes

Why do my quantum group books avoid homotopical language?

There is certainly a natural homotopical analog of braided tensor category, namely a stable $E_2$ category (ie an $E_2$ object of the $\infty$-category of dg categories, or if you prefer or stable $(\ …
David Ben-Zvi's user avatar
2 votes

Differential Hochschild Cohomology, general tools?

Given any bimodule over a commutative ring (or over a scheme, i.e. coherent sheaf on the product) we can consider its differential part, namely the part supported set-theoretically on the diagonal. Ap …
David Ben-Zvi's user avatar
11 votes

algebraic group G vs. algebraic stack BG

The stack $BG$ only recovers $G$ up to inner automorphisms, not canonically (as suggested by blah) - this can lead to serious issues in families or equivalently over a nonalgebraically closed field, a …
David Ben-Zvi's user avatar