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Session 3. Arithmetic Geometry
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Mixed motives and the unit equation |
Stefan Wewers, Universität Ulm, Germany
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The talk is based on the joint work with Ishai Dan-Cohen
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I will report on recent progress towards implementing a practical algorithm
to solve the unit equation over the S-integers, where S is a finite list of
rational prime numbers. The interesting thing is neither the existence nor
the performance of such an algorithm but rather the math behind it: it is
based on a motivic version of Kim's nonabelian Chabauty method. The question
whether it terminates is related to questions about exhaustion of mixed Tate
motives by iterated integrals (studied by Deligne, Goncharov and Brown), and
to a recent conjecture of Kim.
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