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Chern classes of
vector bundles on arithmetic varieties
Tohru Nakashima and Yuichiro Takeda |
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Vol. 176 (1996), No. 1, 205–216
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Abstract |
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Let be a Hermitian vector bundle on an arithmetic variety X over ℤ. We prove an inequality between the L2-norm of an element in H1(X,F∨) and arithmetic Chern classes of under certain stability condition. This is a higher dimensional analogue of a result of C. Soulé for Hermitian line bundles on arithmetic surfaces. We observe that our result is related to a conjectural inequality of Miyaoka-Yau type. |
Mathematical Subject Classification 2000
Primary: 14G40
Secondary: 14C17, 32L07
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Milestones
Received: 3 January 1995
Published: 1 November 1996
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Authors |
| Tohru Nakashima | |
| Department of Mathematics Tokyo Metropolitan University Minami-Ohsawa 1-1,Hachioji-shi Tokyo 192-03 Japan |
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| http://www.ams.org/journals/tran/1997-349-12/S0002-9947-97-02072-2/home.html | |
| Yuichiro Takeda | |
| Department of Mathematics Kyushu University 744 Motooka Nishi-ku Fukuoka 819-0395 Japan |
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| http://www2.math.kyushu-u.ac.jp/~yutakeda/en/index.html | |
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