Update on Harada’s proof – no error after all
Posted by Andreas Holmstrom on February 4, 2009
In a previous post I wrote that there is a mistake in Masana Harada’s proof of the standard conjectures. Now it seems that I was wrong about this. As James Milne kindly points out in a comment, his paper is indeed misquoted, but the argument of Harada is still valid, because, and I quote, “the Tate conjecture (including num=hom) implies that the category of motives over finite fields is generated by abelian varieties, and so the standard conjectures for abelian varieties over finite fields then implies it for all varieties over finite fields”.
Also, Harada posted a revised version of his second preprint a few days ago, fixing a mistake in the proof of Theorem 6.1.
Apparently the proof of Harada builds on an unsuccessful attempt by Thomason to prove the Tate conjecture. Is there anyone who knows where to find a copy of the original preprint of Thomason?