symmetric monoidal (∞,1)-category of spectra
The Riemann hypothesis or Riemann conjecture is the famous unproved statement that all nontrivial zeros of the Riemann zeta function are on the vertical line $Re(z)=1/2$ in the complex plane.
Analogues of the Riemann hypothesis can be considered for many analogues of zeta functions/L-functions. An important case over the finite fields is called the Riemann–Weil conjecture and was proved by Deligne building on earlier ideas of Weil and Grothendieck. Grothendieck however expected a more natural proof using the (hypothetical) theory of motives.
The suggestion that the Riemann hypothesis might have a proof that is an analogue of Weil’s proof for arithmetic curves over finite fields $\mathbb{F}_q$ but generalized to the field with one element is due to