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Euler System


A mathematical structure first introduced by Kolyvagin (1990) and defined as follows. Let T be a finite-dimensional p-adic representation of the Galois group of a number field K. Then an Euler system for T is a collection of cohomology classes c_F in H^1(F,T) for a family of Abelian extensions F of K, with a relation between c_(F^') and c_F whenever F subset F^' (Rubin 2000, p. 4).

Wiles' proof of Fermat's last theorem via the Taniyama-Shimura conjecture made use of Euler systems.


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References

Kolyvagin, V. A. "Euler Systems." In The Grothendieck Festschrift, Vol. 2 (Ed. P. Cartier et al. ). Boston, MA: Birkhäuser, pp. 435-483, 1990.Rubin, K. Euler Systems. Princeton, NJ: Princeton University Press, 2000.

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Euler System

Cite this as:

Weisstein, Eric W. "Euler System." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EulerSystem.html

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