Classical faithfully flat descent is a powerful technique from algebraic geometry that allows us to prove things about “harder objects” by extending them to “easier objects,” and then coming back down. In this talk, we’ll see how an even richer theory of descent can be obtained by passing to derived categories. We will present the resulting theory of “derived descent” as an entry point to “derived algebraic geometry,” the theory obtained by replacing ordinary commutative rings with homotopical objects called E-infinity rings. Along the way, we’ll give an algebra-forward introduction to spectra as “the derived category of the sphere” and see how the mechanism for doing derived descent is exactly the Adams spectral sequence.
Zoom Link: https://washington.zoom.us/j/92849568892