Algebraic families of E_∞-ring spectra
by
Paulo Lima-Filho
Texax A & M

Using techniques from algebraic geometry, we associate in a simple and functorial way, an E_∞-ring spectrum Z_X to every algebraic variety X. The associated generalized cohomology theory Z^*_X reflects algebraic, geometric, and topological properties of the variety X. E.g., the coefficient ring (cohomology of a point) is precisely the Friedlander-Lawson morphic cohomology L^*H^*(X) of X, and when X is smooth, its product structure coincides with the generalized intersection product on L^*H^*(X). The connected component of 1, the zero-th space of this spectrum, admits another delooping whose associated spectrum M_X carries a total Chern class map (of infinite loop spaces) c_X : K_X → M_X from the holomorphic K-theory spectrum of X. All constructions described functors from the category of algebraic varieties and proper morphisms to the stable category of spectra.

Date received: March 17, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caal-21.