Gross-Hopkins and Hopkins-Gross articles
Chromatic fracture squares, the chromatic tower of a spectrum
Topoi and homotopy sheaves (SGA IV)
"Nilpotent thickening" and formal schemes
Ando's power operations, Ando's thesis
Rezk's model cat of model cats (complete Segal spaces)
Dieudonne modules, crystalline cohomology
Rezk's logarithm in power operations, Hecke operators
The difference between formal schemes and Ind-schemes
Displays, windows, and p-divisible groups
"Zariski-locally, f.g. proj. modules are free." What does Zariski-locally even mean on a module? :(
The underlying spaces of spec R and spf W(R) are the same when p is (globally) nilpotent on R
"Verscheibung"? "vehr-shee-bung." W(R) -> W(R)
Spectral localization -- Adams discusses spectral completion, which is not the same
Geometric interpretation of "ramified"
K(n) and E(n) spectra, transchromatic phenomena
Lurie's machine, his survey of elliptic cohomology
Hopf algebroids, their duals, and their cohomology
Old preprint of A-H-S paper with the lazy construction of C_K CP^infty_E, old A-H paper about the interaction of formal schemes with topos theory
"v_n self maps" and Devinatz-Hopkins-Smith
The Singer transfer, THH and EO(n)
Zink's big theorem: p-divisible groups are equivalent to displays, which can be locally represented as matrices of Witt vectors
Other topologies on schemes (flat, etale?)
Geometric and stacky points of moduli spaces / stacks? Reinterpretation with homotopy sheaves? (spec k maps in?)
Morava stabilizer group, Morava K-theory
Transchromatic phenomena and Behrens' diagram of CP^infty_E / S_E
"A group algebra is a Hopf algebra." What's the comultiplication?
Points of a scheme look like maps spec k -> S. Points coupled with a tangent vector look like spec k -> spec k[e]/e^2 -> S.
A coherent geometric definition of MU, and a brief proof of the algebraic <-> geometric correspondence
Proof that the next chromatic theory is _not_ oriented by a connected cover of BU
Tangent space to a functor
Building Ext-like cohomologies with internal Hom objects. Specialization to formal groups and \underline{C}^k(F; G)
Lubin-Tate cohomology spectra, using Lurie's machine to build theories over Z[u_1, ..., u_{h-1}^^_{p, u_{h-1}} instead of Z_(p)[[u_1, ..., u_{h-1}]]
Period maps, Gross-Hopkins period maps, crystalling period maps, periods of elliptic curves