23,688 reputation
464178
bio website wwwmath.uni-muenster.de/u/…
location Münster, Germany
age 27
visits member for 4 years, 9 months
seen yesterday

I am interested in the interactions between algebraic geometry and category theory. More specifically, I "model" algebraic geometry on cocomplete symmetric monoidal categories.

Here is a link to my PhD thesis. Comments are welcome.

Email: [my last name] [at] uni-muenster.de


20h
awarded  Nice Question
1d
comment Classification of rings satisfying $a^4=a$
I've just seen your edit. Thank you, I will look at it!
2d
comment Open covering of the Hilbert functor of points
On the other hand, I don't want to disturb authors will silly questions.
2d
accepted Open covering of the Hilbert functor of points
2d
answered Open covering of the Hilbert functor of points
2d
comment Classification of rings satisfying $a^4=a$
In his book "Modules Over Commutative Regular Rings", Pierce studies as an example rings satisfying $a^n=a$ and their corresponding structure sheaves. But does the book also offer a classification?
2d
comment Classification of rings satisfying $a^4=a$
Hm, $\mathcal{X}$ is equivalent to the category of boolean rings with an action of $C_2$. Is there a direct algebraic way to see that this is $\mathcal{R}$?
Sep
27
comment Classification of rings satisfying $a^4=a$
Yes, I've studied this result and its proof in detail. Probably the shortest and quickest proof ($\approx$ one page) is given in "Elementary proofs of a theorem of Wedderburn and a theorem of Jacobson" by Nagahara and Tominga.
Sep
27
revised Classification of rings satisfying $a^4=a$
added 347 characters in body; edited tags
Sep
27
comment Classification of rings satisfying $a^4=a$
Thanks, but that seems to me what I already know. I am interested in a more explicit classification (or even better, an equivalence of categories).
Sep
27
revised Classification of rings satisfying $a^4=a$
added 490 characters in body
Sep
27
asked Classification of rings satisfying $a^4=a$
Sep
15
awarded  Popular Question
Sep
13
comment When does sheaf cohomology commute with arbitrary direct sums?
Direct sums are filtered colimits of finite direct sums. And finite direct sums are no problem.
Sep
10
comment Canonical presentation of pro-modules over pro-rings
The maps $M_{j+1} \to M_i$ are surjective. It follows easily that each projection $\widehat{M} \to M_j$ is surjective (construct inverse images recursively). Hence, also $\alpha_j$ is surjective.
Sep
10
comment Canonical presentation of pro-modules over pro-rings
From $K_{ji} = M_{j+i} I_{ij}$ for all $i$ we only get $\widehat{K_j} = \varprojlim_i \, (M_{j+i} \cdot I_{ji})$, but why does this equal $\varprojlim_i \, M_{j+i} \cdot \varprojlim_i \, I_{ji} = \widehat{M} \widehat{I_j}$? Again, $\subseteq$ is unclear.
Sep
10
comment Canonical presentation of pro-modules over pro-rings
Thank you. But $\widehat{K_j} = \widehat{I_j} \widehat{M}$ is unclear to me (and clearly this is a direct reformulation of the claim). How do you prove $\subseteq$?
Sep
8
comment Canonical presentation of pro-modules over pro-rings
Sure, the isomorphisms belong to the data. A morphism $M \to N$ is a family of morphisms $M_i \to N_i$ compatible with the isomorphisms. Actually all this follows from the definition $\mathcal{M} := \varprojlim_i \, \mathsf{Mod}(A_i)$.
Sep
8
asked Canonical presentation of pro-modules over pro-rings
Aug
30
comment A short proof for $\dim(R[T])=\dim(R)+1$
R. Gilmer is the author, but of which paper?