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dc.contributor.author | MINAMIDE, Arata | en |
dc.contributor.author | TSUJIMURA, Shota | en |
dc.date.accessioned | 2023-07-18T01:43:23Z | - |
dc.date.available | 2023-07-18T01:43:23Z | - |
dc.date.issued | 2023-06 | - |
dc.identifier.uri | http://hdl.handle.net/2433/284397 | - |
dc.description.abstract | Let p, l be prime numbers. In anabelian geometry for p-adic local fields [i.e., finite extension fields of the field of p-adic numbers], many topics have been discussed. In the present paper, we generalize two of the topics --discovered by S. Mochizuki-- to more general complete discrete valuation fields. One is the mono-anabelian reconstruction, under a certain indeterminacy, of the cyclotomic rigidity isomorphism between the usual cyclotome Ẑ(1) associated to a p-adic local field and the cyclotome constructed, in a purely group-theoretic way, from [the underlying topological group structure of] the absolute Galois group of the p-adic local field. The other is the Neukirch-Uchida-type result, i.e., the field-theoreticity of an outer isomorphism between the absolute Galois groups of p-adic local fields that preserves the respective ramification filtrations. For our generalizations, we first discuss l-local class field theory for Henselian discrete valuation fields with strongly l-quasi-finite residue fields [i.e., perfect fields such that the maximal pro-l quotients of the absolute Galois groups of their finite extension fields are isomorphic to Ẑl] of characteristic p via Artin-Tate's class formation. This theory enables us to reconstruct the l-cyclotomes from the absolute Galois groups of such fields. With regard to cyclotomic rigidity, under a certain assumption, we establish mono-anabelian group/monoid-theoretic reconstruction algorithms for cyclotomic rigidity isomorphisms associated to Henselian discrete valuation fields with quasi-finite residue fields [i.e., perfect residue fields whose absolute Galois groups are isomorphic to Ẑ]. As an application of the reconstructions of cyclotomic rigidity isomorphisms, we determine the structure of the groups of Galois-equivariant automorphisms of various algebraically completed multiplicative groups that arise from complete discrete valuation fields with quasi-finite residues. Moreover, as a byproduct of the argument applied in this determination [especially, in the positive characteristic case], we also determine, in a generalized situation, the structure of a certain indeterminacy “(Ind2)” that appears in S. Mochizuki's inter-universal Teichmüller theory. With regard to the Neukirch-Uchida-type result, by combining the reconstruction result of p-cyclotomes above [in the case where l = p] with a recent result due to T. Murotani, together with a computation concerning norm maps, we prove an analogous result for mixed characteristic complete discrete valuation fields whose residue fields are [strongly] p-quasi-finite and algebraic over the prime fields. | en |
dc.language.iso | eng | - |
dc.publisher | Research Institute for Mathematical Sciences, Kyoto University | en |
dc.publisher.alternative | 京都大学数理解析研究所 | ja |
dc.subject | 11S20 | en |
dc.subject | 11S31 | en |
dc.subject | anabelian geometry | en |
dc.subject | local class field theory | en |
dc.subject | Henselian discrete valuation field | en |
dc.subject | quasi-finite field | en |
dc.subject | cyclotomic rigidity | en |
dc.subject | Neukirch-Uchida theorem | en |
dc.subject.ndc | 410 | - |
dc.title | Anabelian Geometry for Henselian Discrete Valuation Fields with Quasi-finite Residues | en |
dc.type | other | - |
dc.type.niitype | Preprint | - |
dc.identifier.spage | 1 | - |
dc.identifier.epage | 68 | - |
dc.textversion | author | - |
dc.identifier.artnum | RIMS-1973 | - |
dc.sortkey | 1973 | - |
dc.address | Research Institute for Mathematical Sciences, Kyoto University | en |
dc.address | Research Institute for Mathematical Sciences, Kyoto University | en |
dc.relation.url | https://www.kurims.kyoto-u.ac.jp/preprint/index.html | - |
dcterms.accessRights | open access | - |
datacite.awardNumber | 20K14285 | - |
datacite.awardNumber.uri | https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20K14285/ | - |
jpcoar.funderName | 日本学術振興会 | ja |
jpcoar.awardTitle | 局所体に対する遠アーベル幾何学の発展 | ja |
出現コレクション: | 数理解析研究所プレプリント |
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