Push-forwards in oriented cohomology theories of algebraic varieties, by Ivan Panin and Alexander Smirnov

Notions of a cohomology theory and an oriented cohomology theory for algebraic varieties are introduced, push-forwards for projective morphisms are constructed and a Riemann-Roch theorem for ring operations between oriented theories is proved. An explicit formula for the Todd genus related to a ring operation is given. The theory is illustrated by motivic cohomology, algebraic K-theory, algebraic cobordism theory and by other examples.

Ivan Panin <panin@pdmi.ras.ru>
Alexander Smirnov <smirnov@paycash.ru>