- Nishida's theorem
- References
- Further reading
In algebraic topology, the nilpotence theorem gives a condition for an element of the coefficient ring of a ring spectrum to be nilpotent, in terms of complex cobordism. It was conjectured by {{harvtxt|Ravenel|1984}} and proved by {{harvtxt|Devinatz|Hopkins|Smith|1988}}. Nishida's theorem{{harvtxt|Nishida|1973}} showed that elements of positive degree of the homotopy groups of spheres are nilpotent. This is a special case of the nilpotence theorem.References- {{Citation | last1=Devinatz | first1=Ethan S. | last2=Hopkins | first2=Michael J. | authorlink2=Michael J. Hopkins | last3=Smith | first3=Jeffrey H. | title=Nilpotence and stable homotopy theory. I | doi=10.2307/1971440 | mr=960945 | year=1988 | journal=Annals of Mathematics |series=Second Series | issn=0003-486X | volume=128 | issue=2 | pages=207–241| jstor=1971440 }}
- {{citation
|doi= 10.2969/jmsj/02540707
|last= Nishida | first= Goro | authorlink = Goro Nishida
|title= The nilpotency of elements of the stable homotopy groups of spheres
|journal= Journal of the Mathematical Society of Japan
|volume= 25
|issue= 4
|year= 1973
|pages= 707–732
|issn= 0025-5645
|mr= 0341485- {{Citation | last1=Ravenel | first1=Douglas C. |authorlink=Douglas Ravenel| title=Localization with respect to certain periodic homology theories | doi=10.2307/2374308 | mr=737778 | year=1984 | journal=American Journal of Mathematics | issn=0002-9327 | volume=106 | issue=2 | pages=351–414| jstor=2374308 }} Open online version.
- {{Citation | last1=Ravenel | first1=Douglas C. | title=Nilpotence and periodicity in stable homotopy theory | url=https://books.google.com/books?isbn=069102572X | publisher=Princeton University Press | series=Annals of Mathematics Studies | isbn=978-0-691-02572-8 | mr=1192553 | year=1992 | volume=128}}
Further reading - http://mathoverflow.net/questions/116663/connection-of-xn-spectra-to-formal-group-laws
2 : Homotopy theory|Theorems in algebraic topology |