E 'Infinite' Ring Spaces and E 'Infinite' Ring Spectra
by J. P. May
Publisher: Springer 1977
Number of pages: 280
The theme of this book is infinite loop space theory and its multiplicative elaboration. This is the appropriate framework for the most structured development of algebraic K-theory, by which we understand the homotopy theory of discrete categories, and one of the main goals of this volume is a complete analysis of the relationship between the classifying spaces of geometric topology and the infinite loop spaces of algebraic K-theory.
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by Daniel Dugger - University of Oregon
This is an expository paper on homotopy colimits and homotopy limits. These are constructions which should arguably be in the toolkit of every modern algebraic topologist. Many proofs are avoided, or perhaps just sketched.
by J. S. Milne
These are the notes for a course taught at the University of Michigan in 1989 and 1998. The emphasis is on heuristic arguments rather than formal proofs and on varieties rather than schemes. The notes also discuss the proof of the Weil conjectures.
by Robin Hartshorne - Springer
The main purpose of these notes is to prove a duality theorem for cohomology of quasi-coherent sheaves, with respect to a proper morphism of locally noetherian preschemes. Various such theorems are already known. Typical is the duality theorem ...
by Boris Botvinnik - University of Oregon
Contents: Important examples of topological spaces; Constructions; Homotopy and homotopy equivalence; CW-complexes and homotopy; Fundamental group; Covering spaces; Higher homotopy groups; Fiber bundles; Suspension Theorem and Whitehead product; etc.