Gregor Bruns
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# 91 Comments

 Mar 30 comment What's the intution behind defining the cotangent sheaf as $\Delta^\ast(\mathscr{I}/\mathscr{I}^2)$? The last two paragraphs of your answer are almost word-for-word the same as Sándor Kovács' answer on MathOverflow: mathoverflow.net/questions/54593/… If you are not Sándor Kovács (I doubt it), then please attribute the explanation to him. Nov 22 comment Is every complex (smooth) manifold a scheme? Actually, if you want $X^{\text{an}}$ to be a smooth manifold, $X$ needs to be a smooth variety. I have never seen the analytification functor for something else than schemes of finite type over $\mathbb{C}$. Jul 29 comment Is this really a typo? If a function $f$ is $C^k$ for $k\geq 1$ then it automatically is $C^1$, too. So the statement is valid. Jul 4 comment Algebraic Solutions to Systems of Polynomial Equations By 'all variables algebraic' you mean one solution will be a tuple of algebraic numbers? Jun 28 comment An affine open neighborhood of a nonsingular point No, it is not. In fact, it is a rich source of counterexamples regarding schemes that are not varieties. Jun 27 comment An affine open neighborhood of a nonsingular point Your $\Gamma(U,\mathcal{O}_X)$ is (by definition of finite type) a finitely generated $k$-algebra, not just a localization of one. Jun 10 comment My sister absolutely refuses to learn math I tend to agree with your last sentences but it is not at all clear to me whether quick learning later on is not actually also a function of having spent large amounts of time in school on the subject. Jun 3 comment Theorems' names that don't credit the right people Which is not at all wrong since the circumflex just denotes a left-out 's' from old French spelling. Dec 20 comment Find all polynomials that fix $\mathbb Q$ and the irrationals For instance, $x^2$ will map $\sqrt{2}$ to $2$, and therefore be a counterexample. Dec 19 comment Difference between a stalk of a sheaf and a fiber of a vector bundle No need to be sorry. Next to each answer, under the arrows for up/downvoting, there is a little check mark. You can just click on the check mark belonging to the answer you like best to accept it. See here for some images explaining the process. Dec 19 comment Difference between a stalk of a sheaf and a fiber of a vector bundle Please consider accepting some answers to your previous questions. People will be less willing to respond if they think you won't appreciate their answers anyway. Dec 16 comment Normality in a group $G$ Please supply some additional information, so that we can help you better. What have you done? Where are you stuck? Dec 13 comment Is $R = Q[x] / (x^4 - 3x^2+ 6x)$ isomorphic to a direct sum of two fields? We would appreciate it to see some thoughts of your own on this. Also, it is a bit rude to command us to prove it. Dec 12 comment Let $G_1. …, G_k$ be any groups and $\sigma \in S_k$ a permutation. Prove the following map defines an isomorphism Think about the inverse of the permutation. Dec 5 comment Is it true that if a graph is n-regular that it must have n+1 vertices? I interpreted that as 'exactly', but you're right, maybe it was meant as 'at least'. Curiously, I didn't consider this, even if I used to draw two cards when someone told me to "Draw one card". Dec 5 comment Is it true that if a graph is n-regular that it must have n+1 vertices? No, it's not true. Google images for "3-regular graph" shows many counterexamples. A very famous one is the Petersen graph. Dec 4 comment Is $\mathbb R^2$ a field? Indeed, every finite-dimensional vector space $V$ over a field $\mathbb{F}$ is isomorphic to $\mathbb{F}^n$, where $n$ is the dimension of $V$. This fact impressed me a lot when I first learned it. Dec 3 comment Conceptual question about equivalence of eigenvectors Yes. The eigenvalue doesn't even need to be $1$. Dec 2 comment Proving that an equation has no natural solutions Wow, this is really clever! Nov 30 comment A set of objects that satisfy $a^2 = \alpha x$ and commute Did you mean to write "with generators $\{x\}\cup Y$"?