I am away from Torsion theory in abelian category for some while. So It might be a stupid question. The definition of torsion pair in category of modules is as follows: Definiti …

Hello, I wonder if the techniques introduced in Neemans paper: "The Grothendieck duality theorem via Bousfield's techniques and Brown representability " can be used to establish V …

I am now learning localization theory for triangulated catgeory(actually, more general (co)suspend category) in a lecture course. I found Verdier abelianization which is equivalent …

It is well known that Beck's theorem for Comonad is equivalent to Grothendieck flat descent theory on scheme. There are several version of derived noncommutative geometry. I wond …

Situation Let $G$ be a finite group and provide $G\text{-mod} := {\mathbb Z}G\text{-mod}$ with the Frobenius structure of ${\mathbb Z}$-split short exact sequences. Denote by $\un …

Today I was wondering about the axioms given by Bernhard Keller for Cosuspended Categories. The axioms of a triangle feel very much like exactness, but not quite. The last axiom a …

Let $G$ be a group $H\leq G$ a subgroup of finite index. Further, let ${\mathcal E}^G_H$ denote the class of those short exact sequences of $G$-modules (over some fixed base ring) …

Let ${\mathcal D}$ be a triangulated category, ${\mathcal C}$ a triangulated subcategory and $Q: {\mathcal D}\to {\mathcal D}/{\mathcal C}$ the corresponding Verdier-localization. …

let $T$ be a triangulated category and $A \to B \to C \to A[1]$ a triangle in $T$ such that for every $A_0 \in T$ the induced long sequence $... \to \hom(A_0,A) \to \hom(A_0,B) \t …

I did not understand number theory or characteristic p-algebraic geometry at all. I just know a little about frobenius homomorphism between two schemes. On the other hand, when I l …

The title pretty much sums it up - but let me give a little bit of background first. In the p-local stable homotopy category (basically one localizes away the torsion spectra whic …

Start with A an abelian category and form the derived category D(A). Take a triangle (not necessarily distinguished) and take it's cohomology. We obtain a long sequence (not necess …

I know of several results to the effect that two triangulated categories are equivalent categories (usually one coming from algebra and one coming from topology). However, it's ne …

Do you know natural examples of triangulated categories (or [presentable] stable $\infty$-categories) which are not compactly generated? (ideally they'd be defined algebraically, b …

Are the derived categories of modular representations of algebraic groups compactly generated? (e.g. consider SL_2 in characteristic 2). Note modular reps of finite groups are comp …