How many posts have you seen affected by this change? I suppose I'm suspicious that so long as users are only passively editing such posts or flagging comments as they come across them, there won't be a flood of flags to mods' inboxes, or of bumped questions to the front page. — Mike Pierce6 hours ago
We know that the morphisms between objects of derived category are roofs. But how to understand them,and how to compute them. For example, we consider the derived category $D(X)$ of a projective variety $X$, then $\Hom(O_X, E^.)=?$ for a complex $E^.$ and why $\Hom(A, B[1])=\Ext^1(A, B)$ for shea...
Consider the following functional:
$$ E_k(f)=\frac{1}{2}\int_{M} \| \bigwedge^k df\|^2 \text{Vol}_{M}.$$
Theorem:
The Euler-Lagrange equation of $E_2$, is $A(\phi)=0$, where $A(\phi) \in \Gamma(\phi^*\TN)$ is defined by
$$ A(\phi)=h_{\phi^*TN}\bigg(\tr_{\TM}\big(d\phi \otimes \del...
The four posts found with \Spec seems to be false positives. (The OP used \Spec without defining the macro - either by mistake or intentionally.)
The same queries return more results for comments - but again, there are some false positives.
These ones seem like they could be caused by the recent change:
@EhudMeir, indeed, my example with the determinant was an example of something else! :-| I'll correct it. if I start with with a $2$-cocycle $\alpha:G\times G\to\CC^\times$, fix $g\in G$ and let $\beta:h\in G_g\mapsto \alpha(g,h)/\alpha(h,g)\in\CC^\times$, I am only being able to prove that $d\beta=\beta^2\smile\beta^2$, no that it is a $1$-cocycle on $G_g$; is that construction treated somewhere? (I can do it if $\alpha:G\times G^{\ad}\to\CC^\times$ is a $1$-cocycle giving an element of $\Ext^1(\ZZ G^\ad,\CC^\times)$, though: is that what you meant?) — Mariano Suárez-ÁlvarezFeb 25 '16 at 18:14
Hartshorne defines a smooth morphism for schemes of finite type over a field $k$. Moreover, he defines "smooth of relative dimension $n$," not just smooth, requiring each $\mathfrak X_{\mathfrak p} \times_{\Spec \kappa(\mathfrak p)} \Spec \overline{\kappa(\mathfrak p)}$ to be equidimensional. Also, I wasn't sure Bruhat-Tits was using standard definitions, so I wanted to clarify what they said. — D_SOct 16 '17 at 21:31
Martin, ok. Then I made a mistake somewhere. Actually I am very interested in an example of a non-noetherian ring $A$ for which $\Spec A$ is discrete. — jmcApr 6 '12 at 8:50
Thans, this really helps. I guess I can now figure out myself whether things like $ \lim_{i \in I} \Spec R_i \ne \Spec \colim_{i \in I} R_i $ are true. — jmcApr 3 '12 at 6:05
Also, I thought that $(f_*\oO_{\Spec B})_\mf{p} = (\oO_{\Spec B})_\mf{q}$ because of the way he defined the morphism of sheaves $f^\sharp$ and the local homomorphisms $\varphi_\mf{p} : A_{\varphi^{-1}}(\mf{p})\rightarrow B_\mf{p}$. Ie, he said "The induced maps $f^\sharp$ on the stalks are just the local homomorphisms $\varphi_\mf{p}$", but these local homomorphisms are only defined for $\mf{p}\in\Spec B$, whereas they should be defined for all $\mf{q}\in\Spec A$, so it seemed like he was saying that as $\mf{p}$ ranges over $\Spec B$, $f(\mf{p})$ ranges over all of $\Spec A$, which is false.. — Will ChenJun 5 '11 at 1:24
$\newcommand{\fF}{\mathcal{F}}$ Sorry to come back to this, but after rereading Hartshorne's definition of a morphism of locally ringed spaces, that even though as $V$ ranges over all open nbhd's of $f(P)$, $f^{−1}(V)$ ranges over a subset of the nbhd's of $P$, he still claims that $\lim_V \oO_X(f^{−1}(V)) = \oO_{X,P}$. (In your addendum to your original response, you said in general this limit, which you wrote as $(f_∗\fF)_{f(x)}$ is not ismorphic to $\fF_x$) — Will ChenJul 28 '11 at 5:28
I am surprised to see how often people use some common marcro names (such as \Hom, \Spec, etc.) in posts and comments - without noticing that what they posted does not render correctly.
When I checked the results from the above queries one by one, it seems that there were more examples of cases when somebody used macro which wasn't defined on the page rather than cases where the incorrect rendering was caused by the recent change.
Even the comment that I linked in the question on meta seems to be example of commenter's mistake. (I should replace ti by a correct example - a comment where the problem was caused by the change to Stack Exchange software.)
I have replaced the "non-example" by the screenshot of a comment by Mariano Suárez-Álvarez - here the problem was genuinely caused by the recent change in the Stack Exchange software.
Of course, if he returns back to the site and also gets his moderator's privileges back, he can edit the comment himself.
@GerhardPaseman It would be a bit tougher, but an editor could find the place on the page where the \newcommand macro is defined (it's gotta be somewhere on the page, right?), and just copy the definition of that macro into the post where the errors are occurring. This would preserve the author's original rendering without guesswork. I can't imagine a user of one of these affected posts wanting their post to have red-highlighted errors rendered in it, although you are correct that that's only an assumption. — Mike Pierce13 hours ago
@MikePierce I do not know how many such posts and comment are there in total - since I cannot think of an easy how to search for all instances of this problem. The examples from MathOverflow that I have found so far are listed in chat - there is not too many of them. (On Mathematics you can find more such cases - some of them have already been edited. But that it very natural, considering that MO is about 10-times smaller.) — Martin Sleziak3 mins ago
Consider the following functional:
$$ E_k(f)=\frac{1}{2}\int_{M} \| \bigwedge^k df\|^2 \text{Vol}_{M}.$$
Theorem:
The Euler-Lagrange equation of $E_2$, is $A(\phi)=0$, where $A(\phi) \in \Gamma(\phi^*\TN)$ is defined by
$$ A(\phi)=h_{\phi^*TN}\bigg(\tr_{\TM}\big(d\phi \otimes \del...
