Formal schemes and formal groups

By N. Strickland. 2000

55 citations recorded by the source corpus.

We set up a framework for using algebraic geometry to study the generalised cohomology rings that occur in algebraic topology. This idea was probably first introduced by Quillen and it underlies much of our understanding of complex oriented cohomology theories, exemplified by the work of Morava. Most of the results have close and well-known analogues in the algebro-geometric literature, but with different definitions or technical assumptions that are often inconvenient for topological applications. We merely put everything together in a systematic and convenient way.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6e0f794a555e768b219d2425ad3154c4ac7cfea8

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Elliptic spectra, the Witten genus and the theorem of the cube (2001, background): “II.4], for example; see also [ Str99a , Sect.”
The stack of formal groups in stable homotopy theory (2007, background): “In particular, every ring R can be considered as a formal scheme over Z and we thus get the category X fs ,R := Xfs,Z/Spf(R) of formal schemes over R .F or varyingR, these categories assemble into an fpqc-stack Xfs over Spec(Z) which we call the stack of formal schemes [ 36 ], Remark 2.58, Propositi”