SL-oriented intersection theory

Marc Levine, Universität Duisburg-Essen

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Passcode: 998749

Classical intersection theories arise from algebraic oriented theories in the motivic stable homotopy category over a field k, SH(k). Examples include intersection theories with values in the Chow ring, the Grothendieck group of algebraic vector bundles, or taking the universal example, algebraic cobordism. These are algebraic versions of complex oriented cohomology, with Voevodsky’s algebraic cobordism spectrum MGL playing the role of MU. For k of characteristic zero, these theories are closely tied to the topology of the complex points of algebraic varieties.  SL-oriented spectra in SH(k)  yield intersection theories that often refine the oriented ones, producing information closely related to quadratic forms, and also saying something about the cohomology of the real points of algebraic varieties. We will give an introduction to these theories, illustrate with some examples currently in use and give some examples of applications to enumerative problems.