Reputation
5,524
Next privilege 10,000 Rep.
Access moderator tools
Badges
1 12 42
Impact
~64k people reached

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.