发表机构
Joint Graduate School of Mathematics for Innovation, Kyushu University; Institute of Mathematics for Industry, Kyushu University; Graduate School for Mathematics, Kyushu University（九州大学数学创新联合研究生院; 九州大学产业数学研究所; 九州大学数学研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究$p$-adic高度配对对局部分裂的依赖性，通过Bloch-Kato对数给出差分公式，并证明在特定条件下至少一个分圆高度配对非平凡。
AI 中文摘要
数域绝对伽罗瓦群的几何$p$-adic表示构造$p$-adic高度配对依赖于一个全局$p$-adic对数以及在$p$以上素数处Hodge滤过的局部分裂。我们研究这些分裂对合适的二维辛自对偶表示（包括在非普通素数且不整除水平处与偶权新形式相关的表示的自对偶扭曲）的依赖性。我们将由Frobenius确定的两个分裂所关联的高度配对之间的差异显式地用局部Bloch-Kato对数表示。作为在$\mathbb{Q}$上的应用，我们证明在附加假设$p$处Frobenius特征值不同且从Bloch-Kato Selmer群在$p$处的局部化映射非零的情况下，两个分圆$p$-adic高度配对中至少有一个是非平凡的。
英文摘要
The construction of a $p$-adic height pairing for a geometric $p$-adic representation of the absolute Galois group of a number field depends on a global $p$-adic logarithm and on local splittings of the Hodge filtrations at the primes above $p$. We study the dependence on these splittings for suitable two-dimensional symplectic self-dual representations, including self-dual twists of representations attached to even-weight newforms at non-ordinary primes not dividing the level. We express the difference between the height pairings associated with the two splittings determined by Frobenius explicitly in terms of local Bloch--Kato logarithms. As an application over $\mathbb{Q}$, we prove that at least one of the two cyclotomic $p$-adic height pairings is non-trivial under the additional assumptions that the Frobenius eigenvalues at $p$ are distinct and the localization map at $p$ from the Bloch--Kato Selmer group is non-zero.
