Weil’s Rosetta stone (or Conjecture):

**Number Theory (1)** | **Curves over Finite Fields (2) ** | **Riemann Surfaces (3) **

Weil wanted to link up these 3 distinct Maths, as in the Langands Program.

Langrands’ original idea on the Left Column (1) Number Theory & the Middle Column (2):

1. He related :**representations of the Galois groups of number fields ** (objects studied in number theory)

to:**automorphic functions** (objects in harmonic analysis).

2. The middle column (2):

Galois group relevant to curves over finite fields.

Also there exists a branch of harmonic analysis for automorphic functions.

3. How to translate column (3) Riemann Surfaces ?

We have to find **geometric analogues of the Galois groups** and **automorphic functions** in the theory of Riemann surfaces.

Next we have to find suitable analogues of the automorphic functions ?

It was a mystery until 1980 solved by the Russian **Vladimir Drinfeld** (Fields medalist for…

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