An unconditional proof of the abelian equivariant Iwasawa main conjecture and applications
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866917859043573760 |
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| author | Johnston, Henri Nickel, Andreas |
| author_facet | Johnston, Henri Nickel, Andreas |
| contents | Let $p$ be an odd prime. We give an unconditional proof of the equivariant Iwasawa main conjecture for totally real fields for every admissible one-dimensional $p$-adic Lie extension whose Galois group has an abelian Sylow $p$-subgroup. Crucially, this result does not depend on the vanishing of any $μ$-invariant. As applications, we deduce the Coates-Sinnott conjecture away from its $2$-primary part and new cases of the equivariant Tamagawa number conjecture for Tate motives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_03186 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | An unconditional proof of the abelian equivariant Iwasawa main conjecture and applications Johnston, Henri Nickel, Andreas Number Theory 11R23, 11R42 Let $p$ be an odd prime. We give an unconditional proof of the equivariant Iwasawa main conjecture for totally real fields for every admissible one-dimensional $p$-adic Lie extension whose Galois group has an abelian Sylow $p$-subgroup. Crucially, this result does not depend on the vanishing of any $μ$-invariant. As applications, we deduce the Coates-Sinnott conjecture away from its $2$-primary part and new cases of the equivariant Tamagawa number conjecture for Tate motives. |
| title | An unconditional proof of the abelian equivariant Iwasawa main conjecture and applications |
| topic | Number Theory 11R23, 11R42 |
| url | https://arxiv.org/abs/2010.03186 |