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