Jesko Hüttenhain
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 Jan 30 revised Making the definition of dual root unambiguous edited title Jan 30 comment Again: Ample and very ample line bundles @JakeLevinson: Thanks a bunch! Jan 30 asked Making the definition of dual root unambiguous Jan 29 comment a closed subset of an algebraic group with a constant tangent space is a coset Aw, too bad. If you post that as an answer, I could at least award the bounty to you without having it go to waste. Jan 19 reviewed Approve Can $\le$ be used insted of < in the definition of continuity? 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 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 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 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.