-3
$\begingroup$

Hartshorne Exercise II. 3.19 (c) is as follows. Prove the following theorem of Chevalley by using Exercise II. 3.19 (a) and (b) and noetherian induction on $Y$. How do we prove this?

Theorem of Chevalley Let $X$ be a scheme. Let $Y$ be a noetherian scheme. Let $f\colon X \rightarrow Y$ be a morphism of finite type. Then $f(Z)$ is constructible in $Y$ for every constructible subset $Z$ of $X$.

  • 11
    This is the third part of this question you have asked on this site only to write an answer to it yourself. I would prefer to see all users make such posts on their personal blogs, rather than making this site a sort of public notebook. If many users did this sort of thing, the site would be much more difficult to use. For this reason I have downvoted this question.2012-12-19
  • 0
    @CarlMummert I waited for someone else to post his original proof, but noone else did. Anyway answering one's own question is perfectly legitimate in this site. Please don't downvote for such a post. It is against the site's policy.2012-12-19
  • 2
    @CarlMummert "Since Stack Overflow launched, we’ve been trying to explain that it’s not just a Q&A platform: it’s also a place where you can publish things that you’ve learned: recipes, FAQs, HOWTOs, walkthroughs, and even bits of product documentation, as long you format it as a question and answer. if you have a question that you already know the answer to if you’d like to document it in public so others (including yourself) can find it later it is OK to ask, and answer, your own question on a relevant Stack Exchange site." http://blog.stackoverflow.com/2012/05/encyclopedia-stack-exchange/2012-12-19
  • 0
    !Makoto Kato: it seems I disagree with their blog post. I do not view this site as a place for people to document new mathematics; there are more appropriate places to do so, such as personal websites and the arXiv.2012-12-19
  • 0
    @CarlMummert If you disagree with the site's policy, I recommend you not to use this site.2012-12-19
  • 10
    !Makoto Kato: It is not this site's policy; the policies of the *math* SE are determined by its users. We are free to decide as a community that we do not welcome a certain type of post even if it is welcome on other SE sites.2012-12-19
  • 11
    To be clear, it is not answering your own question that is the issue. It is using the site as a kind of notebook to record your work. If a user occasionally answers their own question, especially after getting a hint, that is wonderful. But the purpose of the site is not for asking questions that the asker is already able to solve; I feel that distorts the meaning of "question".2012-12-19
  • 0
    @CarlMummert So what kind of problem would it cause to this site if that was the case?2012-12-19
  • 0
    @CarlMummert "We are free to decide as a community that we do not welcome a certain type of post even if it is welcome on other SE sites." Please explain what's wrong with this question. It's OK that you don't like it. Everybody has his preference. However, it cannot be a proper reason for prohibiting such a question.2012-12-19
  • 2
    My original comment in this thread is the explanation for my downvote. The only reason I left the comment was to provide that explanation.2012-12-19
  • 0
    @CarlMummert "If many users did this sort of thing, the site would be much more difficult to use." Please explain why the site would be much more difficult to use.2012-12-20
  • 0
    @CarlMummert I'm waiting for your explanation.2012-12-20
  • 7
    I have explained everything I wish to explain, and there is nothing else that I wish to add at this time.2012-12-20
  • 0
    @CarlMummert "I have explained everything I wish to explain, and there is nothing else that I wish to add at this time." So you don't wish to explain why the site would be much more difficult to use.2012-12-20
  • 1
    @CarlMummert One of my motivations for asking questions in this site is to provide answers for questions by other members by using my questions. http://math.stackexchange.com/questions/43929/why-are-projective-morphisms-closed http://math.stackexchange.com/questions/241711/how-can-i-prove-formally-that-the-projective-plane-is-a-hausdorff-space http://math.stackexchange.com/questions/238239/a-property-of-the-radical-closure-of-a-field2012-12-20
  • 0
    @CarlMummert I opened a meta thread on this issue. http://meta.math.stackexchange.com/questions/6925/whats-wrong-with-this-question2012-12-20
  • 0
    @CarlMummert Since the above meta thread was closed(they said it was not a real question), I opened a new one changing the question. http://meta.math.stackexchange.com/questions/6926/whats-wrong-with-answering-ones-own-question2012-12-21
  • 0
    @CarlMummert I deleted my answers.2012-12-21
  • 0
    @CarlMummert Again, my meta question was closed. This is a new one. http://meta.math.stackexchange.com/questions/6927/do-this-sort-of-questions-would-make-this-site-much-more-difficult-to-use2012-12-21
  • 5
    Insanity: Doing the same thing over and over again and expecting different results. -Albert Einstein2012-12-21
  • 0
    @robjohn I changed the questions to conform to their reasons for close. One reason that it was a duplicate is simply their misunderstanding.2012-12-21
  • 4
    @MakotoKato. **PLEASE** stop polluting the main site with what is *obviously* meta material.2012-12-21
  • 1
    @MarianoSuárez-Alvarez Don't you see that I was trying to bring the issue to meta?2012-12-22
  • 1
    I have voted to close as "too localized", due to: (1) the extremely narrow framing of the question (don't just prove it, but prove it in *this specific way*), (2) the presentation makes it unlikely that anyone actually interested in the question find it, unless they are searching by book/problem number, and (3) Makoto doesn't even need help with the problem, so not only is it unlikely to help future visitors, it is unlikely to help *current* visitors.2012-12-22
  • 0
    Actually, I do sometimes look for algebraic geometry results by searching for the corresponding exercise in Hartshorne...2012-12-23
  • 0
    I'm curious to know who voted to close, except of course Hurkyl.2012-12-23
  • 0
    @Hurkyl "I have voted to close as "too localized"" You seem to completely forget that this is an exercise of Hartshorne. You voted to close his question.2012-12-24
  • 0
    @Makoto: Hartshorne chose to publish his question in a medium other than MSE, and in a setting where the readers are expected to learning rather than teaching.2012-12-24
  • 0
    @Hurkyl "Hartshorne chose to publish his question in a medium other than MSE, and in a setting where the reader is one who is expected to learn rather than to teach." So? Please explain why this is the reason for voting to close his question.2012-12-24
  • 0
    Rest assured, I'm not holding your responsible for Hartshorne's decision to publish expository material in textbook format. However, I do take issue with your approach to MSE as if you're a assigning homework to the community, especially your insistence that answers be provided as if they were students handing in the answers to said homework rather than people offering help. That last point is likely the cause of the comments indicating that people believe you are taking a class, and trying to get people to give you answers that you can copy and submit as your own homework.2012-12-24
  • 0
    As for the reason to close, as I've indicated, I think I believe both the way you have asked the question and the way you are insisting people respond conspire to make the thread unlikely to ever be of use to anybody.2012-12-24
  • 0
    @Hurkyl "as if you're assigning homework to the community, especially your insistence that answers be provided as if they were students handing in the answers to said homework rather than people offering help." As I explained in my comment for Rankeya's answer, his answer does not correctly answer the question. That's why I don't accept it. Are you saying that if someone asks a question which is an exercise of a book, it should be closed?2012-12-24

2 Answers 2