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97国际8297:首师代数论坛系列报告(二十二)

发布日期:2020-12-18点击量:

报告人:Dr. Georg Tamme (University of Regensburg, Germany)

题目:Excision in algebraic K-theory

时间:2020年12月23日(周三)15:30-16:30

Zoom会议ID:863 2126 0358会议密码: 431083

会议链接:https://uni-regensburg.zoom.us/j/86321260358?pwd=anFobjA0czRWVFBWVXJkbEVjUVB1dz09

摘要:

Algebraic K-groups of rings or schemes are interesting invariants that appear in many different areas of mathematics. Unfortunately, computations are often hard because standard tools from homology, like homotopy invariance or certain Mayer-Vietoris sequences, are not available. The classical excision theorem of Bass, Milnor, and Murthy associates to a Milnor square of rings (a cartesian square with surjective horizontal maps) an exact sequence of algebraic K-groups starting with K_1. In this talk I will explain that this sequence extends naturally to a long exact sequence which involves a new `derived’ ring (a dga) naturally associated with the original Milnor square. In fact, this result holds more generally for any so called localizing invariant as for example topological Hochschild homology and it easily implies and improves excision results of Suslin-Wodzicki, Cortinas, and Geisser-Hesselholt. This is joint work with Markus Land.

报告人简介:

Georg Tammestudied in G?ttingen and Regensburg and did his PhD in 2010 (title of the thesis: The relative Chern character and regulators). His advisor was Prof. Guido Kings. After that he spent one year at the California Institute of Technology (Caltech) and his host there was Prof. Matthias Flach. He then returned to Regensburg where he did his habilitation in 2017 (title of the habilitation thesis: K-theory and regulators: Analytic and homotopical methods). From April to September 2017 he was a substitute professor at the University of Munich and since October 2020 he is a substitute professor at the University of Leipzig.His research interest includes arithmetic and algebraic geometry, homotopy theory; in particular, algebraic K-theory, regulators, differential algebraic K-theory, algebraic K-theory of ring spectra, derived algebraic geometry, motivic homotopy theory. He has published nice papers in good journals such as Ann. of Math., Invent. Math., Adv. Math., Compos. Math. and J. Geom. Phys.


论坛组织者:

童纪龙 唐 舜 陈红星

举办单位:

97国际8297 数学科学学院 97国际8297

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