23,934 reputation
566186
bio website wwwmath.uni-muenster.de/u/…
location Münster, Germany
age 27
visits member for 4 years, 10 months
seen 2 hours ago

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


Oct
21
awarded  Good Question
Oct
21
awarded  Popular Question
Oct
19
comment Sexy vacuity …
@AndreasBlass: Wow, this is a very concise definition! We could also say that on a connected space every continuous function should be constant of some value (i.e. factors over $\{\star\}$). But functions on $\emptyset$ have no value.
Oct
16
comment Examples of common false beliefs in mathematics
@Michael: $\mathbb{Z} \subseteq \mathbb{Q}$
Oct
16
revised Examples of common false beliefs in mathematics
added 10 characters in body
Oct
16
awarded  Popular Question
Oct
15
revised A short proof for $\dim(R[T])=\dim(R)+1$
added 247 characters in body
Oct
15
comment A short proof for $\dim(R[T])=\dim(R)+1$
I've read the proof. It is basically the usually one, cites Zariski-Samuel for a result which depends on Krull's Principal Ideal Theorem. My question was not about some proof (which can be found in almost every commutative algebra text), but rather about a very specific proof, using the characterization by T. Coquand and H. Lombardi. => -1
Oct
14
comment Classification of rings satisfying $a^4=a$
A counterexample is given in Arens-Kaplansky, "Topological representations of algebras", Section 8.
Oct
14
comment Classification of rings satisfying $a^4=a$
Meanwhile I have also found a proof for $X \cong G(F(X))$.
Oct
14
comment Classification of rings satisfying $a^4=a$
Arens-Kaplansky couldn't use the language of functors etc., but what they did is to show that the functor from the algebraic side to the geometric side is fully faithful. They didn't do anything in the other direction, and also didn't prove a duality result. This could be new (... until I finally find a paper where this has been done?).
Oct
14
comment Classification of rings satisfying $a^4=a$
I am very stupid, or at least forgetful. In the paper "Topological representation of algebras" (1947), which I already read several years ago, Arens and Kaplansky give exactly this classification of $4$-rings in terms of $C_2$-actions. And the proof is very simple, one just extends scalars to $\mathbb{F}_4$, where classification is simple, and then one does (what is nowadays called) descent.
Oct
14
comment Theme of Isbell duality
I've read that objects which belong to two concrete categories at once are called schizophrenic. Usually schizophrenic objects induce adjunctions.
Oct
14
accepted Classification of rings satisfying $a^4=a$
Oct
14
comment The quotient stack $[\mathbb{A}^n / \mathrm{GL}_n]$
Thank you for adding the picture.
Oct
14
accepted The quotient stack $[\mathbb{A}^n / \mathrm{GL}_n]$
Oct
13
awarded  Nice Question
Oct
13
accepted Concise definition of subobjects
Oct
13
comment The quotient stack $[\mathbb{A}^n / \mathrm{GL}_n]$
Yes. What is the stabilizer group scheme of the non-zero point?
Oct
13
comment Classification of rings satisfying $a^4=a$
I am still not convinced. I don't see any embedding without using some actions. If Neil's answer is correct (which I believe more and more), then the classification in terms of closed subsets would mean, roughly, that any $C_2$-action on a Stone spaces splits outside the closed subset of fixed points, where I call a $C_2$-space split iff it is isomorphic to $Y \coprod \sigma Y$ for some space $Y$. I don't see any reason why there should be such a splitting. And this is also where cohomology might show obstructions.