Pairings like that between automorphic varieties and Galois groups are identified as dualities. They propose that diverse classes of objects mirror each other, which will allow mathematicians to check possibly a single regarding the other.
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-functions interprets into a geometric duality that makes sense in the geometric Langlands program and originates inside the duality between energy and magnetism. Physics and arithmetic grow to be echoes of each other, in a means that echoes throughout the Langlands application.
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Yiannis Sakellaridis and two coauthors posted a 451-website page manuscript this summer time that forges key new links among geometry and arithmetic.
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