28 Answers votes newest views recent 17Non-commutative algebraic geometry (3) 17Books you would like to see translated into English. 14What would a “moral” proof of the Weil Conjectures require? 10“Algebraic” topologies like the Zariski topology? 8Precise definition of a scheme (Key question: How to define an open subfunctor without resorting to classical scheme theory) 7Is there an analogue Beilinson-Bernstein localization for quantized enveloping algebra 7Most striking applications of category theory? 6“Every scheme as a sheaf” references? 6Collecting various theories on toy examples: Projective space 6Applications of Noncommutative Geometry 5Canonical topology on the category of schemes? 5Homological Algebra for Commutative Monoids? 5The importance of EGA and SGA for “students of today” 4equivalence of Grothendieck-style versus Cech-style sheaf cohomology 4Bimodules in geometry 4When does the sheaf direct image functor f_* have a right adjoint? 3Assumptions on the category C for sheafification of C-valued presheaves 3Why is it a good idea to study a ring by studying its modules? 3Presheaves as limits of representable functors? 3Functorial characterization of morphisms of schemes (2) 3TDO basic facts reference request 2characterization of a submodule 2How much theory works out for “almost commutative” rings? 2What is an algebraic group over a noncommutative ring? 1Tate Cohomology via Stable Categories 1Several Topos theory questions 0Does sheafification preserve sheaves for a different topology? 0A toy example of a tensor triangulated category?