Oriented bivariant theory II- Algebraic cobordism of $S$-schemes -

Abstract

This is a sequel to our previous paper of oriented bivariant theory [14]. In 2001 M. Levine and F. Morel constructed algebraic cobordism ${\Omega }_{\ast }(X)$ for schemes $X$ over a field $k$ in an abstract way and later M. Levine and R. Pandhairpande reconstructed it more geometrically. In this paper in a similar manner we construct an algebraic cobordism ${\Omega }^{\ast }(X\stackrel{{\pi }_X}{\to }S)$ for a scheme $X$ over a fixed scheme $S$ in such a way that if the target scheme $S$ is the point $pt=\mathrm{Spec}k$, then ${\Omega }^{-i}(X\stackrel{{\pi }_X}{\to }pt)$ is isomorphic to Levine-Morel's algebraic cobordism ${\Omega }_i(X)$

35 pages; any comments are welcome

References in corpus (2)

• Bivariant Algebraic Cobordism
• Derived algebraic cobordism