MIT Topology Seminar: Toward higher chromatic analogs of tmf

MIT Topology Seminar

Monday, September 26, 2005
Room 2-142, 4:30pm

Doug Ravenel will speak on:

Toward higher chromatic analogs of tmf

Abstract: This talk is closely related to Mark Behrens' talk of 2 weeks ago. TMF is a spectrum constructed using elliptic curves, and the link between elliptic curves and stable homotopy theory is the theory of 1-dimensional formal group laws. The height of a FGL attached to an elliptic curve is at most 2, so TMF gives infomation about v_2-periodic phenomena, but does not take us deeper into the chromatic tower. A curve of genus g has a g-dimensional FGL (the formal completion of its Jacobian) attached to it, and there are examples where this FGL is known to a 1-dimensional summand of larger height. A suitable moduli space of such curves could conceivably lead to an analog of tmf.