Weil conjectures 2: Functional equation

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This is the second lecture about the Weil conjectures. We show that the Riemann-Roch theorem implies the rationality and functional equation of the zeta function of a curve over a finite field.

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At 4:45 it is mentioned that the finite number of classes of a given degree is equivalent to the finiteness of classes in an imaginary qudratic field, why is this so? What is the underlying imaginary quadratic field and how is it connected to the Weil divisor class group?

markoskarameris

Désde México vivo por las Mathematics. Thanks you.

xjyzzhv

L égalité x^y=y^x équivalent e^ylnx=e^xlny équivalent lnX/X=lny/y soit la fonction F(z)=lnz/z l étude la croisant et décroissant la dérive donne f'(z)=1/z^2(1-lnz) la fonction croisant sur l intervalle [0:e] et décroissant sur l intervalle [e:l infini] et s annule pour z=1la fonction et monotone sur les deux intervalles montre que quelques soit X appartient [1:e] il existe y appartient [e: l infini] telle que lnX/X=lny/y équivalent x^y=y^x d ou il existe l infini des solutions de cette égalité dans R pour les entière il existe 2 appartient l intervalle [1:e] puisque pour l ensemble R il existe l infini de couple (x;y) réaliser l égalité'

thdgus

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