Coates-Wiles homomorphisms and Iwasawa cohomology for Lubin-Tate extensions
Coates-Wiles homomorphisms and Iwasawa cohomology for Lubin-Tate extensions
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DOI：
10.1007/978-3-319-45032-2_12
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发表时间：
2015-03
期刊：
影响因子：
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通讯作者：
P. Schneider;O. Venjakob
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文献类型：
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作者：
P. Schneider;O. Venjakob
对于Fontaine的p-分圆塔，建立了局部Iwasawa上同调的一个刻划，其系数为局部Galois表示Vin项的-算子作用于所附的标模D（V）.本章利用Galois表示与-模之间范畴的Kisin-Ren/方丹等价性和[20，33]的推广部分，将方丹的结果推广到有限扩张Lof上任意Lubin-Tate塔的情形。此外，我们还证明了一种显式的互反律，该互反律计算了由Lubin-Tate形式群的Tate模T的对偶扭成的乘法群在上的库默映射，该互反律是用科尔曼幂级数和附加模表示的.证明是基于一个推广的Schmid-Witt剩余公式。最后，我们将Bloch和Kato [3]定理2.1的显式互易律推广到我们的情形，用广义Coates-Wiles同态表示T上的Bloch-Kato指数映射，其中Lubin-Tate特征标描述T上的Galois作用。
For thep-cyclotomic tower ofFontaine established a description of local Iwasawa cohomology with coefficients in a local Galois representationVin terms of the-operator acting on the attached etale-moduleD(V). In this chapter we generalize Fontaine’s result to the case of arbitrary Lubin–Tate towersover finite extensionsLofby using the Kisin–Ren/Fontaine equivalence of categories between Galois representations and-modules and extending parts of [20, 33]. Moreover, we prove a kind of explicit reciprocity law which calculates the Kummer map overfor the multiplicative group twisted with the dual of the Tate moduleTof the Lubin–Tate formal group in terms of Coleman power series and the attached-module. The proof is based on a generalized Schmid–Witt residue formula. Finally, we extend the explicit reciprocity law of Bloch and Kato [3] Theorem 2.1 to our situation expressing the Bloch–Kato exponential map forin terms of generalized Coates–Wiles homomorphisms, where the Lubin–Tate characterdescribes the Galois action onT.