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I have been asked to write a mathscinet review for Atsushi Moriwaki's Arakelov Geometry book:

http://www.ams.org/bookstore-getitem/item=mmono-244

I could do the review the standard way in a day or two, but then I would pretty much duplicate the contents of existing reviews, on Zentralblatt by Kleinert, and on the MAA siteby Zaldivar.

These reviews say what the book is about and say that it is very nice, to which I agree (though I have not read it through and have not used any part of it in class).

If there is any way I could write a review which actually adds value to the above reviews, I could use some help, especially since I have not worked in the subject since I learned it first!

Here are my questions:

  1. has any of you used the book in class, or at least worked through it in preparation for using in class and knows what combinations of chapters might constitute good courses?

  2. Can you point out to developments in the subject after 2008 (when the Japanese version was published) and their relationship with what's in this book? (One thing that comes to mind is the non-archimedean approach to finite places, as in the work of Zhang and of Moriwaki).

  3. Can you suggest any other discussion which may be valuable in the review?

thanks and best regards,

Dan

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    $\begingroup$ If you have not read the book, and if you are not going to read the book (but rather ask the MathOverflow community for their advice), why don't you just decline to write a MathSciNet review? If there are MathOverflow users who are familiar with the work, you could suggest those people as alternate reviewers. $\endgroup$
    – Jason Starr
    Commented May 3, 2015 at 18:57
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    $\begingroup$ @Jason. OP said had not read the book THROUGH. That is not reason to decline. He never said he would not read book contrary to what you write. Also sentence "Shall we ask the editors of MathSciNet what they think?" is threatening and very unfriendly. $\endgroup$
    – evgeniamerkulova
    Commented May 3, 2015 at 19:31
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    $\begingroup$ I do want to clarify something that my original post may have left unclear - I do have some time to complete reading the book at the level of detail required for mathscinet. I was hoping for something better (and requiring MORE work) $\endgroup$
    – Dan Abramovich
    Commented May 3, 2015 at 19:56
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    $\begingroup$ I can understand why some think it's an unusual request, but I think it's fine for this question to stay open. Particularly in asking for classroom experiences: gathering and assessing a spectrum of opinion here might lead to valuable information for potential users of the text. Also, something about the fact that the OP (who's a full professor at Brown) is asking under the spotlight of MO, together with the tone of his comments, gives me confidence that he will treat and acknowledge answers with propriety, and only wishes to perform his task honorably (and intends to read the book through!). $\endgroup$
    – Todd Trimble
    Commented May 4, 2015 at 4:14
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    $\begingroup$ The review is now published as MR3244206. Hopefully it shows what I meant. I did get help with (1), (2) and (3) from several colleagues by email correspondence. I was disappointed with math overflow. $\endgroup$
    – Dan Abramovich
    Commented Nov 11, 2015 at 15:45

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