论文标题
混合特性完整估值字段的绝对Galois组之间同态的几何特性，具有完美的残基领域
Geometric properties of homomorphisms between the absolute Galois groups of mixed-characteristic complete discrete valuation fields with perfect residue fields
论文作者
论文摘要
尽管Neukirch-uchida定理的类似物对$ p $ adadic本地领域没有保持原样，但摩西木证明了该定理对绝对galois群体的某种类似物，其后果是$ p $ ad的本地领域。此外，Mochizuki和Hoshi给出了各种（必要的和）足够的条件，以实现$ P $ - 亚种的本地领域的绝对Galois群体之间的同态性，即“几何”（即，源于领域的同态）。在本文中，我们考虑了具有完美残基领域的一般混合特性完整评估领域的类似问题。一个主要结果给出了（必要和）足够的条件，以实现混合特性完整的离散估价场的绝对galois组之间的同态性，而在素数为几何的基本场上，残基字段代数为几何。我们还为这些田地的绝对Galois组之间的同态同构提供了“弱ISOM”的结果。
Although the analogue of the theorem of Neukirch-Uchida for $p$-adic local fields fails to hold as it is, Mochizuki proved a certain analogue of this theorem for the absolute Galois groups with ramification filtrations of $p$-adic local fields. Moreover, Mochizuki and Hoshi gave various (necessary and) sufficient conditions for homomorphisms between the absolute Galois groups of $p$-adic local fields to be "geometric" (i.e., to arise from homomorphisms of fields). In the present paper, we consider similar problems for general mixed-characteristic complete discrete valuation fields with perfect residue fields. One main result gives (necessary and) sufficient conditions for homomorphisms between the absolute Galois groups of mixed-characteristic complete discrete valuation fields with residue fields algebraic over the prime fields to be geometric. We also give a "weak-Isom" anabelian result for homomorphisms between the absolute Galois groups of these fields.
