Abstract: In this talk, I start to consider constructible sheaves on the curve. Guided by the analogy between the curve (associated to an algebraically closed field F in char p) and a classical smooth projective curve over an algebraically closed field, Laurent Fargues made several conjectures about the étale cohomology of the curve. I will explain how to handle these conjecture completely in the prime to p torsion case and how the comparison of étale cohomology of the algebraic curve and the adic curve would imply the p torsion case. If time permits, I’ll explain an approach for proving the last statement (which has an analogy for P1 and gives there a new proof of the comparison).
