Inter-universal geometry と ABC予想 (応援スレ) 46

Inter-universal geometry と ABC予想 (応援スレ) 46at MATH

Inter-universal geometry と ABC予想 (応援スレ) 46 - 暇つぶし2ch731:s the Hodge structure on the cohomology groups. It has been speculated (for example by Manin?) that there should be some kind of ‘Galois group’ whose representations are Hodge structures, (and similarly for mixed Hodge modules vs perverse sheaves, and so on) but this remains mysterious; it may be that a good theory of algebraic geometry over F1 (the would-be “field with one element”) would provide an explanation. Tate twists play an important role in cohomology theories with this dual geometric and arithmetic aspect, allowing one to express Poincare duality canonically, that is, without choosing an orientation of one’s geometric object (scheme, complex manifold, …). 3. References https://arxiv.org/abs/math/0610426 [Submitted on 13 Oct 2006] p-adic etale Tate twists and arithmetic duality Kanetomo Sato Graduate School of Mathematics Nagoya University In this paper, we define, for arithmetic schemes with semistable reduction, p-adic objects playing the roles of Tate twists in etale topology, and establish their fundamental properties. Comments: 66 papges. to appear in Ann. Sci. Ec. Norm. Sup. (4) https://arxiv.org/pdf/math/0610426.pdf https://researchers.chuo-u.ac.jp/Profiles/3/0000248/profile.html?lang=ja 教授サトウ　カネトモ佐藤　周友

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