论文标题
EPSILON常数猜想，用于$ \ Mathbb Z_P^r（1）$的更高维度未受到的曲折
The epsilon constant conjecture for higher dimensional unramified twists of $\mathbb Z_p^r(1)$
论文作者
论文摘要
令$ n/k $为$ p $ - adic数字字段的有限galois扩展名，让$ρ^\ mathrm {nr}：g_k \ to \ mathrm {gl} _r（\ mathbb z_p）$ be $ r $ r $ dimementimentia美元在本文中，我们考虑$ \ mathrm {gal}（n/k）$ - $ p $ -ADIC代表$ t = \ mathbb z_p^r（1）（ρ^\ mathrm {nr}）$的$ pubivariant本地$ε$ -Conjocture。例如，如果$ a $是以$ \ mathbb q_p $定义的ABELIAN品种$ r $，则具有良好的普通减少，那么Tate Module $ t = t_p \ hat a $ a $ a $与正式的$ \ hat $ \ hat a $ a $ a $ a $ a $ as a $ p $ - a $ p $ - ad $ - ad $ aidic表示此表格。我们证明了所有驯服扩展的猜想$ n/k $以及某个弱且大受损扩展的家族$ n/k $。这概括了Izychev和Venjakob在驯服案中的先前工作，以及在弱和疯狂的案件中的作者。
Let $N/K$ be a finite Galois extension of $p$-adic number fields and let $ρ^\mathrm{nr} : G_K \to \mathrm{Gl}_r(\mathbb Z_p)$ be an $r$-dimensional unramified representation of the absolute Galois group $G_K$ which is the restriction of an unramified representation $ρ^\mathrm{nr}_{\mathbb Q_p} : G_{\mathbb Q_p} \to \mathrm{Gl}_r(\mathbb Z_p)$. In this paper we consider the $\mathrm{Gal}(N/K)$-equivariant local $ε$-conjecture for the $p$-adic representation $T = \mathbb Z_p^r(1)(ρ^\mathrm{nr})$. For example, if $A$ is an abelian variety of dimension $r$ defined over $\mathbb Q_p$ with good ordinary reduction, then the Tate module $T = T_p\hat A$ associated to the formal group $\hat A$ of $A$ is a $p$-adic representation of this form. We prove the conjecture for all tame extensions $N/K$ and a certain family of weakly and wildly ramified extensions $N/K$. This generalizes previous work of Izychev and Venjakob in the tame case and of the authors in the weakly and wildly ramified case.
