Reseach on algebraic cycles by cohomology

2014 Fiscal Year Final Research Report

• Project/Area Number: 23340003
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Chuo University
• Principal Investigator: SATO Kanetomo 中央大学, 理工学部, 教授 (50324398)
• Co-Investigator(Renkei-kenkyūsha): ASAKURA Masanori 北海道大学, 大学院理学研究院, 准教授 (60322286) ; KIMURA Shun-ichi 広島大学, 大学院理学研究科, 教授 (10284150) ; SAITO Shuji 東京工業大学, 大学院理工学研究科, 教授 (50153804) ; YAMAZAKI Takao 東北大学, 大学院理学研究科, 教授 (00312794)
• Project Period (FY): 2011-04-01 – 2015-03-31
• Keywords: 代数学 / 整数論 / 数論幾何学 / 代数的サイクル / 代数的K理論 / モチーフ / コホモロジー

Outline of Final Research Achievements

As a tool to study vector bundles on algebraic varieties, we have the notion of Chern class, which measures `how a vector bundle is twisted', in a linear space called cohomology. In this research under report, we start with a naive quiestion concernning `in what kind of cohomology the Chern classes are defined', and formulated a minimal set of axioms for such cohomology. We also proved the Riemann-Roch theorem holds in such cohomology theories.

Free Research Field

代数学