Tame class field theory over local fields
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866915735960289280 |
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| author | Gupta, Rahul Krishna, Amalendu Rathore, Jitendra |
| author_facet | Gupta, Rahul Krishna, Amalendu Rathore, Jitendra |
| contents | For a quasi-projective scheme $X$ admitting a smooth compactification over a local field of residue characteristic $p > 0$, we construct a continuous reciprocity homomorphism from a tame class group to the abelian tame etale fundamental group of $X$. We describe the prime-to-$p$ parts of its kernel and cokernel. This generalizes the higher dimensional unramified class field theory over local fields by Jannsen-Saito and Forre. We also prove a finiteness theorem for the geometric part of the abelian tame etale fundamental group, generalizing the results of Grothendieck and Yoshida for the unramified fundamental group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_02953 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Tame class field theory over local fields Gupta, Rahul Krishna, Amalendu Rathore, Jitendra Algebraic Geometry Primary 14C25, Secondary 14F42, 19E15 For a quasi-projective scheme $X$ admitting a smooth compactification over a local field of residue characteristic $p > 0$, we construct a continuous reciprocity homomorphism from a tame class group to the abelian tame etale fundamental group of $X$. We describe the prime-to-$p$ parts of its kernel and cokernel. This generalizes the higher dimensional unramified class field theory over local fields by Jannsen-Saito and Forre. We also prove a finiteness theorem for the geometric part of the abelian tame etale fundamental group, generalizing the results of Grothendieck and Yoshida for the unramified fundamental group. |
| title | Tame class field theory over local fields |
| topic | Algebraic Geometry Primary 14C25, Secondary 14F42, 19E15 |
| url | https://arxiv.org/abs/2209.02953 |