613 reputation
416
bio website
location Barcelona
age 27
visits member for 2 years, 1 month
seen Aug 2 at 9:03
I'm a PhD student at the Universitat Autònoma de Barcelona.

Jul
4
awarded  Yearling
Jul
2
awarded  Curious
Jun
6
comment Krull dimension of dense extensions
I do not see why... the atomic Boolean algebras seem to have Gabriel dimension 1.
Jun
6
comment Krull dimension of dense extensions
I've added the two definitions
Jun
6
revised Krull dimension of dense extensions
added 1774 characters in body
Jun
6
comment Krull dimension of dense extensions
very interesting, nice proof! Do you have any guess on the Gabriel dimension?
Jun
6
revised Krull dimension of dense extensions
edited body
Jun
5
asked Krull dimension of dense extensions
Apr
28
awarded  Revival
Apr
28
answered Analogy between Lagrange's Theorem and Rank-Nullity Theorem?
Feb
19
comment (Short) Exact sequences with no commutative diagram between them
I think $C_2$ should be $A_2$, I'm not allowed to edit just one symbol. Nice answer!
Oct
31
awarded  Benefactor
Oct
31
accepted Do constructible sets have Krull dimension?
Oct
31
comment Do constructible sets have Krull dimension?
Cormulier: Are you aware of the following paper: tandfonline.com/doi/pdf/10.1081/AGB-120004483 it seems to be strongly connected to what you are mentioning. Do you know further references on the topic?
Oct
27
comment (Co)localization of the derived category
Yes, you are right again, thanks! It really seems that there is a decomposition of the category in a direct sum of the category in "connected components" (each "connected component" of the category is given by objects whose injective envelope is the clique of a given indecomposable injective... ). I'm formalizing a proof. This seems to solve completely my question
Oct
27
comment (Co)localization of the derived category
let me also say that it would be safe to assume that the category is also locally Noetherian (otherwise this notion of link is not sufficient...)
Oct
27
comment (Co)localization of the derived category
yes you are right, it's not just what I have written. Again in a semi-artinian Grothendieck category, you have a link between two indecomposable injectives $E$ and $E′$ if $Hom(E,E′)\neq 0$ or $Hom(E′,E)\neq 0$. The Gabriel spectrum becomes a (undirected) graph where the edges are the links I have just defined. The clique of E is the connected component of E in this graph. Sorry for the mistake before... (this is not exactly the usual terminology of, say, Jategaonkar but I tried to give some natural notion of links and cliques in more "categorical" terms)
Oct
27
accepted (Co)localization of the derived category
Oct
27
comment (Co)localization of the derived category
yes I agree, thanks for the nice "minimal" example. This happens essentially because there is a link between the indecomposable injective object which cogenerates $\tau$ and the other indecomposable injective. Now, suppose that you are in a semi-artinian Grothendieck category (just to make it simpler) and that, instead of being cogenerated by a single indecomposable injective, $\tau$ is cogenerated by an entire clique of indecomposable injectives (all the injectives that have non-trivial morphisms to or from a given indecomposable injective). Any thought in this more restricted setting?
Oct
27
revised (Co)localization of the derived category
added 2 characters in body