Let N/K be a Galois extension of p-adic number fields and let V be a de Rham representation of the absolute Galois group GK of K. In the case V = ℚp(1), the equivariant local 𝜖-constant conjecture describes the compatibility of the equivariant Tamagawa number conjecture with the functional equation of Artin L-functions and it can be formulated as the vanishing of a certain element RN/K in K0(ℤp[G], ℚpc[G]); a similar approach can be followed also in the case of unramified twists ℚp(1)(ρnr) of ℚp(1) (see [W. Bley and A. Cobbe, The equivariant local 𝜀-constant conjecture for unramified twists of ℤp(1), Acta Arith. 178(4) (2017) 313–383; D. Izychev and O. Venjakob, Equivariant epsilon conjecture for 1-dimensional Lubin–Tate groups, J. Théor. Nr. Bordx. 28(2) (2016) 485–521]). One of the main technical difficulties in the computation of RN/K arises from the so-called cohomological term CN/K, which requires the construction of a bounded complex CN,T• of cohomologically trivial modules which represents RΓ(N,T) for a full GK-stable ℤp-sublattice T of V. In this paper, we generalize the construction of CN,T• in Theorem 2 of [W. Bley and A. Cobbe, The equivariant local 𝜀-constant conjecture for unramified twists of ℤp(1), Acta Arith. 178(4) (2017) 313–383] to the case of a higher dimensional T.

中文翻译：

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RΓ(N,T) 的代表，用于 ℤpr(1) 的高维扭曲

让ñ/ķ是一个伽罗瓦扩展p-进数字段并让五是绝对伽罗瓦群的德拉姆表示Gķ的ķ. 在这种情况下五 = ℚp(1), 等变局部𝜖-常数猜想描述了等变多摩川数猜想与Artin函数方程的相容性大号-函数，它可以表述为某个元素的消失Rñ/ķ在ķ0(ℤp[G], ℚpC[G]); 在没有分支的情况下也可以采用类似的方法ℚp(1)(ρ天然橡胶)的ℚp(1)（参见 [W. Bley 和 A. Cobbe，等变局部𝜀- 不变的猜想ℤp(1),阿里斯学报。 178(4) (2017) 313–383；D. Izychev 和 O. Venjakob，一维 Lubin-Tate 群的等变 epsilon 猜想，J.泰尔。编号。博德克斯。 28(2) (2016) 485–521])。计算中的主要技术难点之一Rñ/ķ源于所谓的上同调项Cñ/ķ，这需要构造一个有界复合体Cñ,吨•代表的上同调平凡模块RΓ(ñ,吨)对于一个完整的Gķ-稳定的ℤp-亚晶格吨的五. 在本文中，我们概括了Cñ,吨•在 [W. Bley 和 A. Cobbe，等变局部𝜀- 不变的猜想ℤp(1),阿里斯学报。 178(4) (2017) 313–383] 到更高维的情况吨.