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A representative of RΓ(N,T) for higher dimensional twists of ℤpr(1)
International Journal of Number Theory ( IF 0.5 ) Pub Date : 2021-04-20 , DOI: 10.1142/s1793042121500706
Alessandro Cobbe 1
Affiliation  

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 = p(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(p[G], pc[G]); a similar approach can be followed also in the case of unramified twists p(1)(ρnr) of p(1) (see [W. Bley and A. Cobbe, The equivariant local 𝜀-constant conjecture for unramified twists of p(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 p-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 p(1), Acta Arith. 178(4) (2017) 313–383] to the case of a higher dimensional T.

中文翻译:

RΓ(N,T) 的代表,用于 ℤpr(1) 的高维扭曲

ñ/ķ是一个伽罗瓦扩展p-进数字段并让是绝对伽罗瓦群的德拉姆表示Gķķ. 在这种情况下 = p(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/ķķ0(p[G], pC[G]); 在没有分支的情况下也可以采用类似的方法p(1)(ρ天然橡胶)p(1)(参见 [W. Bley 和 A. Cobbe,等变局部𝜀- 不变的猜想p(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,代表的上同调平凡模块RΓ(ñ,)对于一个完整的Gķ-稳定的p-亚晶格. 在本文中,我们概括了Cñ,在 [W. Bley 和 A. Cobbe,等变局部𝜀- 不变的猜想p(1),阿里斯学报。 178(4) (2017) 313–383] 到更高维的情况.
更新日期:2021-04-20
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