Pairings like that in between automorphic varieties and Galois groups are identified as dualities. They propose that various classes of objects mirror each other, which permits mathematicians to review both 1 with regards to another.
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The geometric Langlands application started during the early 1980s when Vladimir Drinfeld and Alexander Beilinson instructed a kind of 2nd-buy duality. Drinfeld and Beilinson proposed that Langlands’ duality amongst Galois teams and automorphic forms may be interpreted being an analogous duality between two sorts of geometric objects.
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