Fortnightly links (87)

Tarig Abdelgadir, Daniel Chan: Tensor stable moduli stacks and refined representations of quivers is a really interesting preprint on how to circumvent the failure of Rosenberg's reconstruction theorem for algebraic stacks using (a shadow of) the monoidal structure. Cool stuff!

Dmitri Orlov: Finite-dimensional differential graded algebras and their geometric realizations is a really interesting construction for the geometricity problem for smooth and proper dg algebras (which in general is still open): it is shown that for every finite-dimensional dg algebra its derived category can be embedded in the derived category of a smooth projective variety. Cool stuff!

Do you think there is a positive or negative answer to the general case?

Roland Abuaf: Derived invariance of the numbers $\mathrm{h}^{0,p}(X)$ delivers what its title says: using the dual notion of his notion of homological units Abuaf shows that at least a whole row of Hodge numbers in the Hodge diamond are a derived invariant. The paper has been withdrawn.

Here the general consensus is I guess that there will be a positive answer. I'm looking forward to seeing a positive answer here! It seems that the general consensus is inching more and more towards a negative answer. Let me know if you have a counterexample!