トポロジー火曜セミナー

過去の記録 ~08/06次回の予定今後の予定 08/07~

開催情報 火曜日 17:00~18:30 数理科学研究科棟(駒場) 056号室
担当者 河野 俊丈, 河澄 響矢, 北山 貴裕, 逆井卓也
セミナーURL http://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html
備考 Tea: 16:30 - 17:00 コモンルーム

2014年07月22日(火)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Jesse Wolfson 氏 (Northwestern University)
The Index Map and Reciprocity Laws for Contou-Carrere Symbols (ENGLISH)
[ 講演概要 ]
In the 1960s, Atiyah and Janich constructed the families index as a natural map from the space of Fredholm operators to the classifying space of topological K-theory, and showed it to be an equivalence. In joint work with Oliver Braunling and Michael Groechenig, we construct an analogous index map in algebraic K-theory. Building on recent work of Sho Saito, we show this provides an analogue of Atiyah and Janich's equivalence. More significantly, the index map allows us to relate the Contou-Carrere symbol, a local analytic invariant of schemes, to algebraic K-theory. Using this, we provide new proofs of reciprocity laws for Contou-Carrere symbols in dimension 1 (first established by Anderson--Pablos Romo) and 2 (established recently by Osipov--Zhu). We extend these reciprocity laws to all dimensions.