Abstract We prove an analogue of Horrocks’ splitting theorem for Segre–Veronese varieties building upon the theory Tate resolutions on products projective spaces.

We give a survey, for non-experts, of the non-abelian Lubin-Tate theory, a cohomological realization of the local Langlands correspondence over p-adic fields. As its proof at the moment (mostly given by the work of Harris-Taylor [HT]) requires global techniques using certain Shimura varieties, we will treat the arithmetic geometry of these Shimura varieties, including some of the recent develop...

We study certain formal group laws equipped with an action of the cyclic order a power 2. construct C2n-equivariant Real oriented models Lubin–Tate spectra Eh at heights h=2n?1m and give explicit formulas C2n-action on their coefficient rings. Our construction utilizes equivariant associated norms bordism theory MUR, our work examines height Hill–Hopkins–Ravenel MUR.

An elliptic curve over a field K is a projective nonsingular genus 1 curve E over K along with a chosen K-rational point O of E, which automatically becomes an algebraic group with identity O. If K has characteristic 0, the n-torsion of E, denoted E[n], is isomorphic to (Z/nZ) over K. The absolute Galois group GK acts on these points as a group automorphism, hence it acts on the inverse limit l...