The algebraic p-adic L-function and isogeny between families of Galois representations
The algebraic p-adic L-function and isogeny between families of Galois representations
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代数p进L函数以及伽罗瓦表示族之间的同构
DOI：
10.1016/j.jpaa.2007.10.001
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发表时间：
2008-06
影响因子：
0.8
通讯作者：
T. Ochiai
中科院分区：
文献类型：
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作者：
T. Ochiai
本文给出了变形环R上给定Galois表示族的两个不同格的代数p-adic L-函数的比较公式。这推广了Schneider [P. Schneider，The mu-invariant of isogenies，J. Indian Math.Soc.52（1987）159-170]和Perrin-Riou [B. Perrin-Riou，Variation de la fonnel Lp-adique par isogénie，Algebras number theory，Adv. Stud. Pure Math. 17（1989）347-358]，其中R是分圆岩泽代数。回想一下，我们在[T。Ochiai，A generalization of the科尔曼map for希达deformations，The Amer.J.Math.125（2003）849-892; T.李文，李文。Ochiai，关于双变量岩泽主猜想，Compos。142（2006）1157-1200]，并且我们通过这些工作获得了足够的理解。通过将我们的公式应用到希达的几乎普通的变形，我们更好地理解了两个变量岩泽理论的剩余可约的情况下，格的选择不再是唯一的。
In this paper, we give a formula to compare the algebraic p-adic L-functions for two different lattices of a given family of Galois representations over a deformation ring R. This generalizes a classical comparison formula by Schneider [P. Schneider, The mu-invariant of isogenies, J. Indian Math. Soc. 52 (1987) 159–170] and Perrin-Riou [B. Perrin-Riou, Variation de la fonction Lp-adique par isogénie, Algebraic number theory, Adv. Stud. Pure Math. 17 (1989) 347–358], for which R is the cyclotomic Iwasawa algebra. Recall that we studied the two-variable Iwasawa theory for residually irreducible nearly ordinary Hida deformations in [T. Ochiai, A generalization of the Coleman map for Hida deformations, The Amer. J. Math. 125 (2003) 849–892; T. Ochiai, Euler system for Galois deformation, Ann. Inst. Fourier 55 (2005) 113–146; T. Ochiai, On the two-variable Iwasawa Main Conjecture, Compos. Math. 142 (2006) 1157–1200] and we acquired sufficient understanding through these works. By applying our formula to Hida’s nearly ordinary deformations, we understand better the two-variable Iwasawa theory for residually reducible cases, where the choice of lattices is not unique anymore.