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edited Apr 18, 2013 at 16:14

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The Bloch-Kato conjectureand Beilinson's conjectures. Here is an extremely pleasant write up on that http://www.claymath.org/programs/summer_school/2009/BellaicheNotes.pdf http://www.math.jussieu.fr/~nekovar/pu/mot.pdf http://wwwmath.uni-muenster.de/u/peter.schneider/publ/pap/beilin.ps

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created Apr 18, 2013 at 16:08

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The Bloch-Kato conjecture. Here is an extremely pleasant write up on that http://www.claymath.org/programs/summer_school/2009/BellaicheNotes.pdf