3,291 reputation
630
bio website nullteilerfrei.de
location Germany
age 28
visits member for 2 years, 10 months
seen 19 hours ago

I'm a PhD student with research interests in Algebraic Geometry, Algebraic Complexity Theory and Geometric Invariant Theory.


Jan
17
awarded  Popular Question
Jan
14
comment $f_\ast \mathcal{O}_X$ locally free iff $X$ Cohen-Macaulay
Well sure, the converse also holds. It is essentially the same argument. You might need that finite morphisms are affine.
Jan
13
comment $f_\ast \mathcal{O}_X$ locally free iff $X$ Cohen-Macaulay
It is indeed. You can reformulate the first statement to "$R$ is CM $\Leftrightarrow$ All localizations at maximal ideals of $R$ are CM $\Leftrightarrow$ All localizations at prime ideals of $R$ are CM". Hence, even if $y$ corresponds only to a point and not a closed point, localization at $y$ will be CM.
Jan
13
reviewed Approve suggested edit on How to prove that $n^7\equiv n^3\mod40,\forall n\in\mathbb{Z}$
Jan
13
answered $f_\ast \mathcal{O}_X$ locally free iff $X$ Cohen-Macaulay
Jan
11
revised An example of a $P$-primary ideal $I$ satisfying $I^2 = IP$
formatting cleanup
Jan
10
awarded  Custodian
Jan
10
reviewed Close Tell a sequence in which there comes three consecutive even numbers after three odd numbers indefinitely?
Jan
10
reviewed Approve suggested edit on Let $U$ and $V$ be any two open sets with $U\cap V=\emptyset$ and $F\subset U\cup V$. Show that there is an integer $n$ with $F_n\subset U\cup V$.
Jan
10
comment P/B is isomorphic to the projective line $\mathbb{P}^1$
I am confused. I thought Borel subgroups of an algebraic group are the minimal parabolics. Wikipedia agrees with me. That would mean $P/B$ is trivial. Also, what do you mean by "containing a root"? A root is usually a character of a maximal torus in $B$, not an element of the group.
Jan
10
reviewed Approve suggested edit on How to calculate a complicated geometrical series?
Jan
9
comment Criterion for etaleness
How much additional constraints are you willing to empose on your rings $A$ and $B$? Can they be Noetherian by any chance? Or even finitely generated $\Bbbk$-algebras over an algebraically closed field? Alright, I might be asking for a lot there. But still, anything beyond commutative?
Jan
7
revised Coplanar codition
slightly fixed and unified the notation
Jan
7
comment Why $\mathcal{O}_{\mathbb{P}^n}(1)$ is a line bundle?
I once wrote a little blog post about why vector bundles and locally free sheaves are the same. It might help.
Dec
29
comment Abstract nonsense proof of snake lemma
@MarkS. is correct. I primarily want to understand the reasoning in Borceux' book. I hope you don't take my downvote as a personal offense, but this is precisely what I did not want.
Dec
29
accepted Any affine algebraic group is linear.
Dec
29
comment Any affine algebraic group is linear.
This looks really good! Thanks for tending to this very old question of mine and giving a satisfying answer.
Dec
6
awarded  Taxonomist
Dec
6
awarded  Good Question
Dec
2
accepted Infinite group with no maximal normal solvable subgroup