2011-02-19, 06:33 | #1 |
Feb 2011
2 Posts |
Deligne's work on the Weil conjectures
For the Frobenius automorphism , Grothendieck proved that the zeta function is equivalent to
where the polynomial on the L-adic cohomology group . In his 1974 paper, Deligne proved that all zeros of lie on the critical line of complex numbers with real part , a geometric analogue of the Riemann hypothesis. My question is that if Deligne proved the Riemann hypothesis using étale cohomology theory, then how come the Riemann hypothesis is still an open problem? |
2011-02-19, 11:30 | #2 |
(loop (#_fork))
Feb 2006
Cambridge, England
3×7^{2}×43 Posts |
The Weil conjectures refer to the zeta functions of algebraic varieties over finite fields, as defined at http://en.wikipedia.org/wiki/Weil_co...il_conjectures
These were called zeta functions by analogy with the Riemann zeta function, but they're not the same thing. |
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