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Higher Arithmetic K-theory (代数的整数論とその周辺 研究集会報告集)
| Content Provider | Semantic Scholar |
|---|---|
| Author | Yuichiro, Takeda 雄一郎, 竹田 |
| Copyright Year | 2003 |
| Abstract | The aim of this paper is to provide a new definition of higher K-theory in Arakelov geometry and to show that it enjoys the same formal properties as the higher algebraic K-theory of schemes. LetX be a proper arithmetic variety, that is, letX be a regular scheme which is flat, proper and of finite type over Z, the ring of integers. In the research on arithmetic Chern characters of hermitian vector bundles on X, Gillet and Soulé defined the arithmetic K0-group K̂0(X) of X [10]. It can be viewed as an analogue in Arakelov geometry of the K0-group of vector bundles on a scheme. After the advent of K̂0(X), its higher extension was discussed in some papers, such as [5, 6, 15]. In these papers one common thing was suggested that higher arithmetic K-theory should be obtained as the homotopy group of the homotopy fiber of the Beilinson’s regulator map. That is to say, it was predicted that there would exist a group KMn(X) for each n ≥ 0 satisfying the long exact sequence |
| Starting Page | 89 |
| Ending Page | 98 |
| Page Count | 10 |
| File Format | PDF HTM / HTML |
| Volume Number | 1324 |
| Alternate Webpage(s) | https://faculty.math.illinois.edu/K-theory/0561/arith.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0204321v1.pdf |
| Alternate Webpage(s) | http://www.math.illinois.edu/K-theory/0561/arith.pdf |
| Alternate Webpage(s) | http://www.math.uiuc.edu/K-theory/0561/arith.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
