Research on Mixed motives and regulator on algebraic K-theory

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540001
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Hokkaido University
• Principal Investigator: ASAKURA Masanori 北海道大学, 理学(系)研究科(研究院), 准教授 (60322286)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: レギュレーター / 混合モチーフ

Outline of Final Research Achievements

We studied motives, which are the objects arising from cohomology groups of algebraic varieties, and got some nice results. More precisely, we studied the periods of motives with complex multiplication and the regulator as its extension intensively. In particular, we got nice description in terms of special values of generalizaed hypergeometric functions. We hope that our results brings interesting progress on the Beilinson conjecture on special values of L-functions. This is a joint work with Noriyuki Otsubo at Chiba university. We also got a result on the conjecture of Gross and Deligne on the periods of motives with complex multiplication. This is a joint work with Fresan at ETHZ.

Free Research Field

数論幾何学