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