2022-05-26T06:02:51Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000056542021-03-01T16:25:21Zp-進数体上のモチフィックホモロジーと類体論Motivic Homology and Class Field Theory over p-adic FieldsUzun, Mecit Kerem11758University of Tokyo (東京大学)博士(数理科学)The main goal of this thesis is to give a description of the abelian étale fundamental group of a smooth (not necessarily proper) variety U over a p-adic field k in case U has a smooth compactification that has a good reduction over k. The group SK1 in the proper case is replaced with the motivic homology. We first construct a map between motivic homology and étale cohomolgy with compact supports where in certain degrees the latter one can be idetified with abelian étale fundamental group using Poincare duality. Following Yamazaki we construct a reciprocity map and calculate the kernel and cokernel using known results on the vanishing of Kato homology.thesis2013-03-252013-03-25application/pdfapplication/pdfhttps://repository.dl.itc.u-tokyo.ac.jp/record/5654/files/UzunM_25_3_PhD_a.pdfhttps://repository.dl.itc.u-tokyo.ac.jp/record/5654/files/UzunM_25_3_PhD_b.pdfeng