共查询到20条相似文献,搜索用时 15 毫秒
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2.
E. V. Ferens-Sorotskiy 《Journal of Mathematical Sciences》2009,161(4):597-601
It is known from the Lubin-Tate theory that a Lubin–Tate formal group can be constructed by its distinguished isogeny, and
an arbitrary power series (with a few restrictions) can be taken as such an isogeny. A similar statement is also known for
Honda formal groups. In the present article, a similar statement is proved in detail for p-typical formal groups in the so-called small ramification case. It is also proved that as a distinguished homomorphism, in
general, one cannot take a polynomial. Bibliography: 6 titles. 相似文献
3.
In the paper, formal groups over the rings of integers of σ-fields are studied. These fields were constructed by the first
author in a previous paper. They are a generalization of the inertia field of a classical local field to an arbitrary complete
discrete valuation field of characteristic zero. An analog of Honda’s theory for such formal groups is constructed. The arithmetic
of the group of points in an extension of a σ-field that contains sufficiently many torsion points is studied. Using the classification
of formal groups and the arithmetic results obtained, an explicit formula for the Hilbert pairing for formal groups over σ-fields
is proved. Bibliography: 16 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 319, 2004, pp. 5–58. 相似文献
4.
S. V. Vostokov 《Journal of Mathematical Sciences》1990,52(3):3133-3141
One considers the structure of the group of the points of a formal group and its Lutz filtration as a Galois module in an
extension without higher ramification of a local field. Making use, on one hand, of Honda's theory on the classification of
formal groups over complete local rings and, on the other hand, of a generalization to formal groups of the Artin-Hasse function,
one constructs effectively an isomorphism between the group of points and some given additive free Galois module. In particular,
in the multiplicative case one gives a new effective proof of Krasner's theorem on the normal basis of the group of principal
units of a local field in extensions without higher ramification.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR,
Vol. 160, pp. 182–192, 1987. 相似文献
5.
Alexandru Buium 《Compositio Mathematica》2003,139(2):197-237
The quotient of a Shimura curve by the isogeny equivalence relation is not an object of algebraic geometry. The paper shows how this quotient space becomes a geometric object in a more general geometry obtained from 'usual algebraic geometry', by adjoining a new operation; this operation looks like a 'Fermat quotient' and should be viewed as an arithmetic analogue of usual derivations. 相似文献
6.
Let K be a finitely generated field of transcendence degree 1 over a finite field. Let M be a t-motive over K of characteristic p0, which is semisimple up to isogeny. The isogeny conjecture for M says that there are only finitely many isomorphism classes of t-motives M′ over K, for which there exists a separable isogeny M′→M of degree not divisible by p0. For the t-motive associated to a Drinfeld module this was proved by Taguchi. In this article we prove it for the t-motive associated to any direct sum of Drinfeld modules of characteristic p0≠0. 相似文献
7.
Jeng-Daw Yu 《Mathematische Annalen》2009,343(1):53-78
We study the variation of the unit roots of members of the Dwork families of Calabi–Yau varieties over a finite field by the
method of Dwork–Katz and also from the point of view of formal group laws. A p-adic analytic formula for the unit roots away from the Hasse locus is obtained.
This work was supported in part by Professor N. Yui’s Discovery Grant from NSERC, Canada. 相似文献
8.
HUANG MingDeh 《中国科学 数学(英文版)》2013,56(7):1421-1427
The discrete logarithm problem is analyzed from the perspective of Tate local duality. Local duality in the multiplicative case and the case of Jacobians of curves over p-adic local fields are considered. When the local field contains the necessary roots of unity, the case of curves over local fields is polynomial time reducible to the multiplicative case, and the multiplicative case is polynomial time equivalent to computing discrete logarithm in finite fields. When the local field does not contains the necessary roots of unity, similar results can be obtained at the cost of going to an extension that contains these roots of unity. There was evidence in the analysis that suggests that the minimal extension where the local duality can be rationally and algorithmically defined must contain the roots of unity. Therefore, the discrete logarithm problem appears to be well protected against an attack using local duality. These results are also of independent interest for algorithmic study of arithmetic duality as they explicitly relate local duality in the case of curves over local fields to the multiplicative case and Tate-Lichtenbaum pairing (over finite fields). 相似文献
9.
This paper considers hyperbolic formal groups, which come from the elliptic curve theory, in the context of the theory of formal modules. In the first part of the paper, the characteristics of hyperbolic formal groups are considered, i.e., the explicit formulas for the formal logarithm and exponent; their convergence is studied. In the second part, the isogeny and its kernel and height are found; a p-typical logarithm is defined. The Artin–Hasse and Vostokov functions are then constructed; their correctness and main properties are evaluated. 相似文献
10.
James Borger 《Mathematische Annalen》2011,351(4):877-933
11.
We generalise G. and D. Chudnovsky's isogeny criterion for elliptic curves over Q to the case of Abelian varieties of dimension g. The proof is bused on an explicit construction of algebraic parameters of their formal groups. 相似文献
12.
Chris Hurlburt 《Compositio Mathematica》2001,128(1):17-34
An interesting theory arises when the classical theory of modular forms is expanded to include differential analogs of modular forms. One of the main motivations for expanding the theory of modular forms is the existence of differential modular forms with a remarkable property, called isogeny covariance, that classical modular forms cannot possess. Among isogeny covariant differential modular forms there exists a particular modular form that plays a central role in the theory. The main result presented in the article will be the explicit computation modulo p of this fundamental isogeny covariant differential modular form. 相似文献
13.
The Cohen–Macaulay locus of any finite module over a noetherian local ring A is studied, and it is shown that it is a Zariski-open subset of Spec A in certain cases. In this connection, the rings whose formal fibres over certain prime ideals are Cohen–Macaulay are studied. 相似文献
14.
M. C. Bartholomew-Biggs 《International Journal of Mathematical Education in Science & Technology》2013,44(6):857-867
This paper describes a Fortran90 library designed to support the teaching of numerical analysis and its applications. As well as covering traditional material it introduces recent and important ideas in numerical computation such as interval arithmetic and automatic differentiation. The library rests on a module realpac which provides real arithmetic in a range of precisions with a choice of rounding strategies. This, in turn, supports the implementation of an interval arithmetic module intpac. Derived data types and overloaded operations help inexperienced users to interface with unfamiliar data types such as intervals. The library also includes more conventional modules such as lepac for solving linear systems and minpac for nonlinear optimization. These, however, can be enhanced by being linked to more sophisticated tools for sparse matrix handling and automatic differentiation. As well as showing the main structure and scope of the software, the paper mentions some exercises that have successfully been performed by students. 相似文献
15.
For each closed, orientable surface , we construct a local, diffeomorphism invariant trace on the Kauffman bracket skein module . The trace is defined when |t| is neither 0 nor 1, and at certain roots of unity. At t = − 1, the trace is integration against the symplectic measure on the SU(2) character variety of the fundamental group of .
Received: June 2, 2000 相似文献
16.
Motivated by a research on self-dual extended group codes, we consider permutation codes obtained from submodules of a permutation
module of a finite group of odd order over a finite field, and demonstrate that the condition “the extension degree of the
finite field extended by n’th roots of unity is odd” is sufficient but not necessary for the existence of self-dual extended transitive permutation
codes of length n + 1. It exhibits that the permutation code is a proper generalization of the group code, and has more delicate structure
than the group code. 相似文献
17.
François Couchot 《代数通讯》2013,41(1):231-241
It is proved that a commutative ring is clean if and only if it is Gelfand with a totally disconnected maximal spectrum. It is shown that each indecomposable module over a commutative ring R satisfies a finite condition if and only if R P is an Artinian valuation ring for each maximal prime ideal P. Commutative rings for which each indecomposable module has a local endomorphism ring are studied. These rings are clean and elementary divisor rings. It is shown that each commutative ring R with a Hausdorff and totally disconnected maximal spectrum is local-global. Moreover, if R is arithmetic, then R is an elementary divisor ring. 相似文献
18.
Isogenies between elliptic curves play a very important role in elliptic curve related cryptosystems and cryptanalysis. It is widely known that different models of elliptic curves would induce different computational costs of elliptic curve arithmetic, and several works have been devoted to accelerate the isogeny computation on various curve models. This paper studies the case of the Jacobi quartic model, which is a classic form of elliptic curves. A new w-coordinate system on extended Jacobi quartic curves is introduced for Montgomery-like group arithmetic. Explicit formulas for 2-isogenies and odd ℓ-isogenies on the specific curves are presented, and based on the w-coordinate system, the computation of such isogenies could be further simplified. 相似文献
19.
The j-invariants of the quadratic Q-curves without complex multiplicationare studied. Some properties of the norms of these invariantsare shown and a relationship between the field Q(j) and thedegree of an isogeny of the Q-curve to its Galois conjugateis found. In the case when the degree of the isogeny is a primep, some properties of the primes of potentially multiplicativereduction for the Q-curve and of the reduction of j modulo aprime P in Q(j) over p when the Q-curve has potentially goodreduction at P are found. 相似文献
20.
Suppose that M is a finite module under the Galois group ofa local or global field. Ever since Tate's papers [17, 18],we have had a simple and explicit formula for the EulerPoincarécharacteristic of the cohomology of M. In this note we are interestedin a refinement of this formula when M also carries an actionof some algebra A, commuting with the Galois action (see Proposition5.2 and Theorem 5.1 below). This refinement naturally takesthe shape of an identity in a relative K-group attached to A(see Section 2). We shall deduce such an identity whenever wehave a formula for the ordinary Euler characteristic, the keystep in the proof being the representability of certain functorsby perfect complexes (see Section 3). This representabilitymay be of independent interest in other contexts. Our formula for the equivariant Euler characteristic over Aimplies the isogeny invariance of the equivariantconjectures on special values of the L-function put forwardin [3], and this was our motivation to write this note. Incidentally,isogeny invariance (of the conjectures of Birch and Swinnerton-Dyer)was also a motivation for Tate's original paper [18]. I am verygrateful to J-P. Serre for illuminating discussions on the subjectof this note, in particular for suggesting that I consider representability.I should also like to thank D. Burns for insisting on a mostgeneral version of the results in this paper. 2000 MathematicsSubject Classification 19A99, 18G99, 11R34. 相似文献