Results 41 to 50 of about 4,688 (128)
Parity of ranks of Jacobians of curves
Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.Abstract We investigate Selmer groups of Jacobians of curves that admit an action of a non‐trivial group of automorphisms, and give applications to the study of the parity of Selmer ranks. Under the Shafarevich–Tate conjecture, we give an expression for the parity of the Mordell–Weil rank of an arbitrary Jacobian in terms of purely local invariants ...
Vladimir Dokchitser +3 more
wiley +1 more source
Cyclic branched covers of Seifert links and properties related to the ADE$ADE$ link conjecture
Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.Abstract In this article, we show that all cyclic branched covers of a Seifert link have left‐orderable fundamental groups, and therefore admit co‐oriented taut foliations and are not L$L$‐spaces, if and only if it is not an ADE$ADE$ link up to orientation. This leads to a proof of the ADE$ADE$ link conjecture for Seifert links. When L$L$ is an ADE$ADE$
Steven Boyer +2 more
wiley +1 more source
The Iwasawa invariants of Zpd${\mathbb {Z}}_{p}^{\,d}$‐covers of links
Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.Abstract Let p$p$ be a prime number and let d∈Z>0$d\in {\mathbb {Z}}_{>0}$. In this paper, following the analogy between knots and primes, we study the p$p$‐torsion growth in a compatible system of (Z/pnZ)d$({\mathbb {Z}}/p^n{\mathbb {Z}})^d$‐covers of 3‐manifolds and establish several analogues of Cuoco–Monsky's multivariable versions of Iwasawa's ...
Sohei Tateno, Jun Ueki
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On relations between cyclotomic units
Journal of Number Theory, 1972 AbstractLet ax = ln|1 − ξmx| with ξm = e2πim. We consider additive relations Σx = 1m − 1 Cxax = 0 between these numbers. We first give certain necessary and sufficient conditions for the integers Cx in order that such a relation holds. It is then possible to construct an explicit algorithm by means of which one can resolve any given relation ...
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Asymptotic estimates of large gaps between directions in certain planar quasicrystals
Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.Abstract For quasicrystals of cut‐and‐project type in Rd$\mathbb {R}^d$, it was proved by Marklof and Strömbergsson [Int. Math. Res. Not. IMRN (2015), no. 15, 6588–6617; erratum, ibid. 2020] that the limit local statistical properties of the directions to the points in the set are described by certain SLd(R)$\operatorname{SL}_d(\mathbb {R})$‐invariant ...
Gustav Hammarhjelm +2 more
wiley +1 more source
On profinite rigidity amongst free‐by‐cyclic groups I: The generic case
Proceedings of the London Mathematical Society, Volume 130, Issue 6, June 2025.Abstract We prove that amongst the class of free‐by‐cyclic groups, Gromov hyperbolicity is an invariant of the profinite completion. We show that whenever G$G$ is a free‐by‐cyclic group with first Betti number equal to one, and H$H$ is a free‐by‐cyclic group which is profinitely isomorphic to G$G$, the ranks of the fibres and the characteristic ...
Sam Hughes, Monika Kudlinska
wiley +1 more source
Cohomology groups of cyclotomic units
Journal of Algebra, 1992 Let \(d\) be a positive integer, \(p\) an odd prime not dividing \(d\) or \(\varphi(d)\). Set \(\zeta_ n=e^{2\pi i/n}\), \(K_n=\mathbb{Q}(\zeta_{p^{n+1}d})\). Set \(\Delta=\text{Gal}(K_{-1}/\mathbb{Q})\), let \(D\) be the decomposition group of \(\Delta\) for \(p\), and \(k\) the fixed field of \(D\). Let \(G_{m,n}=\text{Gal}(K_m/K_n)\) for \(m>n\geq 0\
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Simple closed curves, non‐kernel homology and Magnus embedding
Journal of Topology, Volume 18, Issue 2, June 2025.Abstract We consider the subspace of the homology of a covering space spanned by lifts of simple closed curves. Our main result is the existence of unbranched covers of surfaces where this is a proper subspace. More generally, for a fixed finite solvable quotient of the fundamental group we exhibit a cover whose homology is not generated by the lifts ...
Adam Klukowski
wiley +1 more source
On cyclotomic units connected with p-adic characters
Journal of the Mathematical Society of Japan, 1985 Let \(p\) be an odd prime and \(K\) an abelian number field containing any primitive \(p\)-th root \(\zeta\) of unity, of degree prime to \(p\). For an even character \(\chi\neq 1\) of the Galois group \(G\) of \(K\) over the rationals, we denote by \(\phi\),\({\bar\phi }\) the \(p\)-adic characters over \(\chi,\chi^{- 1}\omega\) respectively, where \(\
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Representation of units in cyclotomic function fields [PDF]
International Journal of Number Theory, 2019 In this paper, we prove a refinement of Hilbert’s Satz 90 for the [Formula: see text]-cyclotomic function fields, where [Formula: see text] is a monic prime in [Formula: see text]. Our result can be viewed as a function field analogue of Newman’s theorem which is a refinement of Hilbert’s Satz 90 for [Formula: see text].
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