# Etale cohomology approach on $\tau(n)$

Ramanujan's $\tau$ conjecture states that $$\tau(n)\sim O(n^{\frac{11}2+\epsilon})$$ which is a consequence of Deligne's proof of Weil conjectures. Answers in Status of $\tau(n)$ before Deligne tell that best exponent before Deligne reached $\frac{29}5$.

What was it that cohomological approach gave that broke the traditional approach barrier to reach $5.5$ in exponent?

• This is way beyond me. But I once tried to get an overview on Deligne's proof, and I found a survey/expository article by Nick Katz. In his Leitfaden the Ramanujan $\tau$ is one of the nodes. IANA an algebraic geometer, but I would guess that $\tau$ makes an appearance in 11th cohomology of some variety - this is probably not accurate. Anyway, Katz' survey may help you more than it ever helped me. – Jyrki Lahtonen Mar 25 '15 at 20:51