Specialization Method in Krull Dimension two and Euler System Theory over Normal Deformation Rings
| Autor: | Kazuma Shimomoto, Tadashi Ochiai |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Conjecture
Mathematics::Commutative Algebra Mathematics - Number Theory General Mathematics Euler system Commutative Algebra (math.AC) Mathematics - Commutative Algebra Ring of integers Combinatorics Mathematics - Algebraic Geometry Number theory Torsion (algebra) FOS: Mathematics Finitely-generated abelian group Krull dimension Number Theory (math.NT) Algebraic Geometry (math.AG) Mathematics |
| Popis: | The aim of this article is to establish the specialization method on characteristic ideals for finitely generated torsion modules over a complete local normal domain R that is module-finite over $${\mathcal {O}}[[x_1,\ldots ,x_d]]$$ , where $${\mathcal {O}}$$ is the ring of integers of a finite extension of the field of p-adic integers $${\mathbb {Q}}_p$$ . The specialization method is a technique that recovers the information on the characteristic ideal $${\text {char}}_R (M)$$ from $${\text {char}}_{R/I}(M/IM)$$ , where I varies in a certain family of nonzero principal ideals of R. As applications, we prove Euler system bound over Cohen–Macaulay normal domains by combining the main results in Ochiai (Nagoya Math J 218:125–173, 2015) and then we prove one of divisibilities of the Iwasawa main conjecture for two-variable Hida deformations generalizing the main theorem obtained in Ochiai (Compos Math 142:1157–1200, 2006). |
| Databáze: | OpenAIRE |
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