共查询到20条相似文献,搜索用时 15 毫秒
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Sylvain Brochard 《Mathematische Annalen》2009,343(3):541-602
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Jean-François Jaulent 《Archiv der Mathematik》2018,111(6):569-578
We formulate a general conjecture on the characteristic polynomials of S-decomposed T-ramified Iwasawa modules over the cyclotomic \(\mathbb {Z}_\ell \)-extension of a number field. We show that this conjecture is equivalent to the conjunctions of the classical conjectures of Leopoldt and of Gross-Kuz’min. We so extend a result of semi-simplicity of Greenberg and, by the way, an isomorphism of Kuz’min. 相似文献
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Olivier Teulié 《Monatshefte für Mathematik》2001,75(5):169-176
In this paper, we prove that for any real number ξ, which is not an algebraic number of degree , there exist infinitely many real algebraic units α of degree n + 1 such that . We also show how the flexibility of H. Davenport and W. M. Schmidt’s method allows to replace, with the same exponent of approximation, units of degree over Z (i.e. elements α with both α and integral over Z) by units of degree over a finite intersection . 相似文献
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Armand Borel 《Commentarii Mathematici Helvetici》1955,29(1):27-39
Sans résumé
A Monsieur H. Hopf, à l’occasion de son soixantième anniversaire 相似文献
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Olivier Teulié 《Monatshefte für Mathematik》2001,134(2):169-176
In this paper, we prove that for any real number ξ, which is not an algebraic number of degree , there exist infinitely many real algebraic units α of degree n + 1 such that . We also show how the flexibility of H. Davenport and W. M. Schmidt’s method allows to replace, with the same exponent of
approximation, units of degree over Z (i.e. elements α with both α and integral over Z) by units of degree over a finite intersection .
(Received 14 March 2000; in revised form 16 November 2000) 相似文献
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Antoine Ducros 《Mathematische Zeitschrift》2013,273(1-2):331-353
Let k be a complete, non-Archimedean field and let X be a k-analytic space. Assume that there exists a finite, tamely ramified extension L of k such that X L is isomorphic to an open polydisc over L ; we prove that X is itself isomorphic to an open polydisc over k. The proof consists in using the graded reduction (a notion which is due to Temkin) of the algebra of functions on X, together with some graded counterparts of classical commutative algebra results : Nakayama’s lemma, going-up theorem, basic notions about étale algebras, etc. 相似文献
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This work falls within the theory of linear forms in logarithms over a connected and commutative algebraic group, defined over the field of algebraic numbers
. Let G be such a group. Let W be a hyperplane of the tangent space at the origin of G, defined over
, and u be a complex point of this tangent space, such that the image of u by the exponential map of the Lie group G(ℂ) is an algebraic point. Then we obtain a lower bound for the distance between u and W⊗ℂ, which improves the results known before and which is, in particular, the best possible for the height of the hyperplane W. The proof rests on Baker’s method and Hirata’s reduction as well as a new arithmetic argument (Chudnovsky’s process of variable change) which enables us to give a precise estimate of the ultrametric norms of some algebraic numbers built during the proof.
Mathematics Subject Classification (2000) 11J86, 11J20, 14L10 相似文献
Mathematics Subject Classification (2000) 11J86, 11J20, 14L10 相似文献
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