Put an AMS offprint (of my paper) on my academic page
The Sherpa/Romeo database is a great resource to find out what kind of re-use the journals allow. In your case, it seems that you can put online the final version of the paper that you submitted to them post-refereeing (with a statement like "published in..."), but not your offprint or the version which is on the publisher website. This is slightly inconvenient because the page numbers will differ, but it is the most common arrangement in mathematics.

The database is only indicative, though: the only legally binding terms are the ones in the copyright transfer agreement that you signed prior to publication, after your paper was accepted (they had you sign one, right?). Read the small print.

This is the theory --- in practice, I have never heard of publishers going after authors for putting the wrong pdf online, at least in mathematics. In general the AMS as a publisher is considered a Good Guy, so I would advise you to respect their requests anyway.