This fortnight's links are not very fortnightly actually. But they are interesting links.
Katrina Honigs, Derived equivalence, Albanese varieties, and the zeta functions of 3-dimensional varieties: an important link between the theory of motives and the study of derived categories is given by Orlov's conjecture. It says that derived equivalent varieties have isomorphic motives. Evidence for this conjecture can be given by showing that derived equivalent varieties have equal motivic invariants, and this preprint is of this sort: it shows that the local zeta function (which is made up of the number of points over all finite fields living above the base finite field) is indeed the same for derived equivalent varieties of dimension up to three. Cool!
commalg.org surveys: in case you desperately need something interesting to read, this list is a good place to start.
Alex Youcis, Reductive groups: a rapid introduction is precisely that, a very good introduction to reductive groups (from a few weeks ago). It focuses nicely on arithmetic aspects of reductive groups, an aspect that I was mostly ignorant about, but which is very interesting indeed! I finally understand the whole business of good and bad reduction of elliptic curves.
- Math the Band, the slightly geeky American cousin (who probably had too much coffee too) of Los Campesinos.