Arithmetic topology in Ihara theory II: Milnor invariants, dilogarithmic Heisenberg coverings and triple power residue symbols

Hikaru Hirano, Masanori Morishita

研究成果: Contribution to journalArticle査読

抄録

We introduce mod l Milnor invariants of a Galois element associated to Ihara's Galois representation on the pro-l fundamental group of a punctured projective line (l being a prime number), as arithmetic analogues of Milnor invariants of a pure braid. We then show that triple quadratic (resp. cubic) residue symbols of primes in the rational (resp. Eisenstein) number field are expressed by mod 2 (resp. mod 3) triple Milnor invariants of Frobenius elements. For this, we introduce dilogarithmic mod l Heisenberg ramified covering D(l) of P1, which may be regarded as a higher analog of the dilogarithmic function, for the gerbe associated to the mod l Heisenberg group, and we study the monodromy transformations of certain functions on D(l) along the pro-l longitudes of Frobenius elements for l=2,3.

本文言語英語
ページ(範囲)211-238
ページ数28
ジャーナルJournal of Number Theory
198
DOI
出版ステータス出版済み - 5 2019

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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