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Local Reciprocity: a Mysterious Map from Number Theory

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Part of the TMS Symposium

I will start by defining the p-adic numbers, the classic example of a local field. I will go on to state the existence of the local reciprocity map and describe the cases for which an explicit formula has been found. I will end by trying to explain what makes it difficult to compute local reciprocity in the remaining cases.

This talk is part of the Trinity Mathematical Society series.

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