## Quasi-coherent sheaves on the moduli stack of formal groups

### Cached

### Download Links

Citations: | 4 - 1 self |

### BibTeX

@TECHREPORT{Goerss_quasi-coherentsheaves,

author = {Paul G. Goerss},

title = {Quasi-coherent sheaves on the moduli stack of formal groups},

institution = {},

year = {}

}

### OpenURL

### Abstract

For years I have been echoing my betters, especially Mike Hopkins, and telling anyone who would listen that the chromatic picture of stable homotopy theory is dictated and controlled by the geometry of the moduli stack Mfg of smooth, one-dimensional formal groups. Specifically, I would say that the height filtration of Mfg dictates a canonical and natural decomposition of a quasi-coherent sheaf on Mfg, and this decomposition predicts and controls the chromatic decomposition of a finite spectrum. This sounds well, and is even true, but there is no single place in the literature where I could send anyone in order for him or her to get a clear, detailed, unified, and linear rendition of this story. This document is an attempt to set that right. Before going on to state in detail what I actually hope to accomplish here, I should quickly acknowledge that the opening sentences of this introduction and, indeed, this whole point of view is not original with me. I have already mentioned Mike Hopkins, and just about everything I’m going to say here is encapsulated in the table in section 2 of [15] and can be gleaned from the notes