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Bloch-Kato Conjectures and Rational Points on Curves

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KAH2 - K-theory, algebraic cycles and motivic homotopy theory

We state the Bloch-Kato conjectures, which relate algebraic K-theory of varieties over number fields and rings of S-integers, to Bloch-Kato Selmer groups, Galois cohomology groups with certain local conditions. We then explain an effective form of Faltings’ Theorem dependent on part of these conjectures. Finally, if time, we mention how Iwasawa theory may be used to verify special cases of these conjectures.

This talk is part of the Isaac Newton Institute Seminar Series series.

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