Fortnightly links (10)

Alberto Canonaco and Paolo Stellari, A tour about existence and uniqueness of dg enhancements and lifts is a really nice overview article on dg enhancements. It was also the basis of a really nice lecture series by Paolo in Bonn a few weeks ago. In this series he also outlined the cool result from the next fortnightly link.

Vadim Vologodsky, Triangulated endofunctors of the derived category of coherent sheaves which do not admit DG liftings is precisely what it says it does: give an example of a non-Fourier-Mukai functor. Such an example was known (in characteristic zero and algebraically closed) by Rizzardo–Van den Bergh, through a really nifty application of deformation theory. The example by Vadim is very different: it is over a finite field and the description of the functor is completely elementary.

Visualization of Frobenius maps is an awesome visualization of what happens with Frobenius for the affine plane over $\mathbb{F}_{64}$, and how rational points on a cubic curve are precisely the fixed points of the Frobenius. There is a nice explanation on the webpage, just scroll down.

The LMFDB is now officially released. I really enjoy seeing online mathematical encyclopaedia, and the scale of this project is particularly impressive. Also interesting is that in some way it is the 21st century version of what are called the Antwerp tables, from the proceedings of the 1972 conference on modular forms in Antwerp, and which was the main reference for some aspects of the numerical data now available in the LMFDB. For more information see also the blogposts at Persiflage and Quomodomcumque.