Motivic stuff

Cohomology, homotopy theory, and arithmetic geometry

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?

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2 Responses to “Update on Harada’s proof – no error after all”

  1. Teh said

    So is the proof correct?

    • homotopical said

      I did not say the proof is correct – I am not competent to judge either way. I have heard various rumours about various (unfounded) opinions people have, but I think the only way to know for sure is to either invest many months of hard work verifying the proof yourself, or wait until it’s submitted to a journal so that some referee actually checks the details.

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