# SECOND CHERN NUMBERS OF VECTOR BUNDLES AND HIGHER ADELES

• Osipov, Denis V. (Steklov Mathematical Institute of Russsian Academy of Sciences)
• 투고 : 2016.08.17
• 심사 : 2016.12.02
• 발행 : 2017.09.30

#### 초록

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 ${\mathbb{Z}}-torsor$ of a locally linearly compact k-vector space. Analogs of certain auxiliary results for the case of an arithmetic surface are also discussed.

#### 과제정보

연구 과제 주관 기관 : Russian Science Foundation

#### 참고문헌

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