Conference "Arithmetic Days"

Adelic Bloch formula for Chern classes

Roman Budylin (Moscow)

Friday 6 April, 10:00-11:00

Резюме

Bloch proves that the second Chern class of a vector bundle with trivial determinant can be obtained by boundary homomorphism for the universal central extension of the sheaf SL(O_X). I use this construction to get an adelic formula for the second Chern class in terms of trivializations in scheme points. I also introduce some extension of St(A) for any ring A by diagonal matrices which allows us to generalize Bloch formula to vector bundles with general determinant. We will also be discuss a generalization of Bloch formula for all c_n of vector bundles with c_i=0, i