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Let k be a p-adic field of odd residue characteristic and let C be a hyperelliptic (or elliptic) curve defined by the affine equation Y
2=h(X). We discuss the index of C if h(X)=ɛf(X), where ɛ is either a non-square unit or a uniformising element in O
k
and f(X) a monic, irreducible polynomial with integral coefficients. If a root θ of f generates an extension k(θ) with ramification index a power of 2, we completely determine the index of C in terms of data associated to θ. Theorem 3.11 summarizes our results and provides an algorithm to calculate the index for
such curves C.
Received: 14 July 1997 / Revised version: 16 February 1998 相似文献
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Tetsuya Uematsu 《Mathematische Zeitschrift》2015,279(3-4):1047-1066
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Toshiro Hiranouchi 《Mathematische Zeitschrift》2010,266(1):107-113
We introduce the idèle class group for quasi-projective curves over p-adic fields and show that the kernel of the reciprocity map is divisible. This extends Saito’s class field theory for projective
curves (Saito in J Number Theory 21:44–80, 1985). 相似文献
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Lei Zhang 《中国科学 数学(英文版)》2018,(1)
In this paper, we recreate the Whittaker-Shintani functions for general linear groups over nonarchimedean fields given by Kato et al. Those generalized spherical functions naturally arise from global zeta integrals of automorphic L-functions. More explicitly, this formula plays a fundamental role in the local calculation over the split places of tensor product L-functions defined by Jiang and Zhang(2014) and the twisted automorphic descents introduced by Jiang and Zhang(2015). 相似文献
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Peter Scholze 《Inventiones Mathematicae》2013,192(3):663-715
We extend our methods from Scholze (Invent. Math. 2012, doi:10.1007/s00222-012-0419-y) to reprove the Local Langlands Correspondence for GL n over p-adic fields as well as the existence of ?-adic Galois representations attached to (most) regular algebraic conjugate self-dual cuspidal automorphic representations, for which we prove a local-global compatibility statement as in the book of Harris-Taylor (The Geometry and Cohomology of Some Simple Shimura Varieties, 2001). In contrast to the proofs of the Local Langlands Correspondence given by Henniart (Invent. Math. 139(2), 439–455, 2000), and Harris-Taylor (The Geometry and Cohomology of Some Simple Shimura Varieties, 2001), our proof completely by-passes the numerical Local Langlands Correspondence of Henniart (Ann. Sci. Éc. Norm. Super. 21(4), 497–544, 1988). Instead, we make use of a previous result from Scholze (Invent. Math. 2012, doi:10.1007/s00222-012-0419-y) describing the inertia-invariant nearby cycles in certain regular situations. 相似文献
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Publications mathématiques de l'IHÉS - 相似文献
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Kanat S. Abdukhalikov 《Designs, Codes and Cryptography》2001,23(3):343-370
Affine invariant and cyclic codes over p-adic numbers and over integers modulo p
d are studied. It has been determined what cyclic codes have an extension that is affine invariant. 相似文献
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Amnon Besser 《Compositio Mathematica》2002,130(2):215-223
The finite nth polylogarithm li
n
(z) /p(z) is defined as
k=1
p–1
z
k
/k
n
. We state and prove the following theorem. Let Li
k
:
p
p
be the p-adic polylogarithms defined by Coleman. Then a certain linear combination F
n
of products of polylogarithms and logarithms, with coefficients which are independent of p, has the property that p
1–n
DF
n
(z) reduces modulo p>n+1 to li
n–1((z)), where D is the Cathelineau operator z(1–z)d/dz and is the inverse of the p-power map. A slightly modified version of this theorem was conjectured by Kontsevich. This theorem is used by Elbaz-Vincent and Gangl to deduce functional equations of finite polylogarithms from those of complex polylogarithms. 相似文献
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Let F be a field finitely generated and of transcendence degree one over a p-adic field, and let ? ≠ p be a prime. Results of Merkurjev and Saltman show that H2(F, µ?) is generated by ?/?-cyclic classes. We prove the “?/?-length” in H2(F, µ?) is less than the ?-Brauer dimension, which Salt-man showed to be three. It follows that all F-division algebras of period ? are crossed products, either cyclic (by Saltman’s cyclicity result) or tensor products of two cyclic F-division algebras. Our result was originally proved by Suresh when F contains the ?-th roots of unity µ?. 相似文献
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O. Casas-Sánchez W. A. Zúñiga-Galindo 《P-Adic Numbers, Ultrametric Analysis, and Applications》2013,5(3):177-193
We study pseudodifferential equations and Riesz kernels attached to certain quadratic forms over p-adic fields. We attach to an elliptic quadratic form of dimension two or four a family of distributions depending on a complex parameter, the Riesz kernels, and show that these distributions form an Abelian group under convolution. This result implies the existence of fundamental solutions for certain pseudodifferential equations like in the classical case. 相似文献
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We prove that a form of finite Galois descent obstruction is the only obstruction to the existence of integral points on integral
models of twists of modular curves over function fields. 相似文献
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Lithuanian Mathematical Journal - We consider simultaneous rational approximations to real and p-adic numbers. We prove that for any irrational number α0 and p-adic number α, there are... 相似文献
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We establish a duality in the cohomology of arbitrary tori over smooth but not necessarily projective curves over a p-adic field. This generalises Lichtenbaum–Tate duality between the Picard group and the Brauer group of a smooth projective
curve.
Received: 28 January 2002 /
Published online: 28 March 2003
Mathematics Subject Classification (2000): 14G20, 14F22, 14L15, 11S25 相似文献
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We give examples of fields elementarily equivalent to a given finite extension of the p-adic numbers but not containing a subfield of finite codimension elementarily equivalent to the p-adics. 相似文献