Isogenies of formal group laws and power operations in the cohomology theories En

A renormalized Riemann-Roch formula and the Thom isomorphism for the free loop space

“…We explain this in section 4.2, after briefly reviewing finite quotients of formal groups, following [Lub67,And95].…”

Engenera

“…The E ∞ structures on these cobordism spectra derive from products and powers of manifolds, and work of Ando, Hopkins, Rezk, and Strickland (and their collaborators, among others) shows that refining maps out of cobordism spectra and related spectra to E ∞ (or H ∞ ) ring maps has implications in geometry as well as topology and stable homotopy theory (see, for example, [2,4,5]). An E ∞ ring structure brings with it many extra tools and much of the work of stable homotopy in the past two decades has involved producing E ∞ ring structures and E ∞ ring maps.…”

HKR characters, $p$-divisible groups and the generalized Chern character

“…For r ≥ 0, we let D n (r) be the representing ring of the functor classifying Drinfeld (Z/p r Z) n -level structures on a deformation of H n (cf. [6,1,27,16]). The ring D n (r) is obtained from E 0 n by adjoining all p r -torsion points of F n in the algebraic closure of the field of fractions of E 0 n .…”

“…, it is connected of height (n + 1) over the stratum X (0) , and is an extension of anétale p-divisible group of height 1 by a p-divisible formal group of height n over the stratum X (1) . Then the attaching map of X (1) to X (0) is important to understand the relationship between the K(n)-local category and the K(n + 1)-local category.…”

“…Then the attaching map of X (1) to X (0) is important to understand the relationship between the K(n)-local category and the K(n + 1)-local category. The connection between extensions of anétale p-divisible group of height 1 by a p-divisible formal group and stable homotopy theory has been discussed in [2, §5]; see also [10,30,31].…”