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We give a construction of the second Chern number of a vector bundle over a smooth projective surface by means of adelic transition matrices for the vector bundle. The construction does not use an algebraic $K$-theory and depends on the canonical $\Z$-torsor of a locally linearly compact $k$-vector space. Analogs of certain auxiliary results for the case of an arithmetic surface are also discussed.
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참고문헌 (16)
참고문헌 신청
A. A. Beilinson / 1988 / Determinant bundles and Virasoro algebras / Comm. Math. Phys 118(4):651~701
J.-L. Brylinski / 2001 / Central extensions of reductive groups by K2 / Publ. Math. Inst. Hautes Études Sci 94:5~85
R. Ya / 2011 / Budylin, Adelic construction of the Chern class / Sb. Math 202(11-12):1637~1659
R. Ya. Budylin / 2013 / Intersections of adelic groups on a surface / Sb. Math 204(11-12):1701~1711
T. Chinburg / 2015 / Higher adeles and non-abelian Riemann-Roch / Adv. Math 281:928~1024
J.-L. Brylinski / 2001 / Central extensions of reductive groups by K2 / Publ. Math. Inst. Hautes Études Sci 94:5~85
R. Ya / 2011 / Budylin, Adelic construction of the Chern class / Sb. Math 202(11-12):1637~1659
R. Ya. Budylin / 2013 / Intersections of adelic groups on a surface / Sb. Math 204(11-12):1701~1711
T. Chinburg / 2015 / Higher adeles and non-abelian Riemann-Roch / Adv. Math 281:928~1024
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