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seen Jun 16 at 15:45

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29
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awarded  Nice Answer
Jun
16
comment Ex 6.7 in Görtz and Wedhorn's AGI
Dear Fang, I think the point of @johnw. 's comment was that there are two authors of the book you link to (Wedhorn as well as Görtz), but your title only mentions one of them. Regards,
Jun
16
answered Hartshorne “Algebraic Geometry” theorem 8.15
Jun
16
comment Prove that $6$ and $2(1+\sqrt{-5})$ do not have a gcd in $\mathbb{Z}[\sqrt{-5}]$
Dear Manolis, That's correct. Regards,
Jun
16
answered Every $A$-mod is flat iff every mod-$A$ is flat.
Jun
16
comment Every $A$-mod is flat iff every mod-$A$ is flat.
Dear Pedro, I went to look for you in chat, but then saw you'd posted your question here. I will post an answer below. Cheers,
Jun
16
awarded  Nice Answer
Jun
16
answered sections of an invertible sheaf, and their support
Jun
16
comment sections of an invertible sheaf, and their support
@yogesh: Dear yogesh, Your comment hints at some confusion that "sections of $\mathcal O(K_{\mathbb P^n})$ vanish on hyperplanes, while the $n$-form has poles on hyperplanes". These statements are not in the tension that you seem to imagine they are. Rather, what this expresses is that if we want to multiply an $n$-form on $\mathbb P^n$ by a rational function in such a way as to get an $n$-form without poles, then this rational function would need to vanish along the locus of poles of the $n$-form. Regards,
Jun
16
comment sections of an invertible sheaf, and their support
Dear yogesh, You may want to look at this answer. Regards,
Jun
16
answered pullback of canonical divisor
Jun
16
comment About globally generated Sheaves
Dear Keenan, You might want to right to Ravi just pointing out this slight ambiguity/error in the problem. Cheers,
Jun
16
comment How do i show that finite abelian group is solvable?
@egreg: Dear egreg, What you call a normal series, most authors would call a subnormal series. Also, a composition series is simply a maximal subnormal series (or, in your terminology, a normal series), i.e. one in which all the successive factors are simple. (Let me suppose I'm working with finite groups, so there are no problems with imagining such maximal subnormal series.) So there is not so much difference between your definition and the OP's. Regards,
Jun
16
comment Are there finite-dimentional unital associative algebras over $\Bbb{C}$ that are not isomorphic to a group algebra $\Bbb{C}[G]$ for finite group G?
Dear Lkzavr, If your second question is "is there a standard way of computing these algebras for particular groups $G$?", then the answer is yes --- you compute the dimensions of the irreps. of $G$ (one way or another). If you have more specific questions about that, you may want to ask them in a separate question. Regards,
Jun
16
comment $f: SL_2(\mathbb{R}) \to GL_4(\mathbb{R})$ show that $Im(f)=SL_4(\mathbb{R})$
Dear lanzariel, This is a special case of the theory of representations of Lie groups and algebraic groups. There are many books that treat this theory; Fulton and Harris is one of my favourite introductions to the theory. And yes, you can get a map to $SL_3$ in the same way. Regards,
Jun
16
comment $f: SL_2(\mathbb{R}) \to GL_4(\mathbb{R})$ show that $Im(f)=SL_4(\mathbb{R})$
Dear lanzariel, The title of your question is misstated. The image will lie in $SL_4$, but won't equal $SL_4$. Regards,