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In this paper, we develop the Euler system theory for Galois deformations. By applying
this theory to the Beilinson-Kato Euler system for Hida’s nearly ordinary modular
deformations, we prove one of the inequalities predicted by the two-variable Iwasawa main
conjecture. Our method of the proof of the Euler system theory is based on non-arithmetic
specializations. This gives a new simplified proof of the inequality between the
characteristic ideal of the Selmer group of a Galois deformation and the...
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