2022-05-20T17:42:00Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000056532021-03-01T16:25:22Z対角的3次曲面のBrauer群の統一的な表示可能性についてUniform Representability of the Brauer Group of Diagonal Cubic SurfacesUematsu, Tetsuya11756University of Tokyo (東京大学)博士(数理科学)The Brauer group of a scheme is an effective tool for studying its arithmetic and geometric properties. For such purposes, we need to know not only the structure of the Brauer group as an abelian group, but also explicit generators such as those represented by norm residue symbols. Yu. I. Manin first studied such problems for diagonal cubic surfaces. He determined the structure of the Brauer group of some diagonal cubic surfaces and found its symbolic generators. In this dissertation, we generalize his result. We introduce the notion of uniformity for generators and prove the following two results: first, diagonal cubic surfaces of a particular form have such uniform generators represented by a norm residue symbol; secondly, in general, diagonal cubic surfaces have no uniform generator. The latter result states that there is a limit to extend the Manin's result stated above.thesis2013-03-252013-03-25application/pdfapplication/pdfhttps://repository.dl.itc.u-tokyo.ac.jp/record/5653/files/UematsuT_25_3_PhD_a.pdfhttps://repository.dl.itc.u-tokyo.ac.jp/record/5653/files/UematsuT_25_3_PhD_b.pdfeng