bio | website | |
---|---|---|
location | Münster, Germany | |
age | 27 | |
visits | member for | 5 years |
seen | Dec 16 at 19:09 | |
stats | profile views | 35,284 |
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
Dec 11 |
awarded | ag.algebraic-geometry |
Nov 18 |
answered | Why are flat morphisms “flat?” |
Nov 18 |
comment |
an easy example of valuation ring which is not noetherian？
Yes. en.wikipedia.org/wiki/… |
Nov 17 |
awarded | Nice Answer |
Nov 8 |
awarded | Good Question |
Nov 3 |
comment |
Sexy vacuity …
A consequence of $\sup(\emptyset)=-\infty$ is that the Krull dimension of the zero ring is $-\infty$. Notice that this is consistent with $\dim(R \times S)=\max(\dim(R),\dim(S))$. Usually rings in which prime ideals are maximal are called zero-dimensional, but this is not quite true: The zero ring is not zero-dimensional, but still every prime ideal is maximal (vacuously). |
Nov 3 |
comment |
Sexy vacuity …
@KevinBuzzard: Defining $|f|$ as the smallest real number such that $f$ maps balls with radius $r$ into balls with radius $|f|r$, for all $r > 0$, should work for all cases, right? |
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 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 $a^4=a$
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. |