Rubin, Karl Stark units and Kolyvagin’s “Euler systems”. (English) Zbl 0752.11045 J. Reine Angew. Math. 425, 141-154 (1992). In his important work on the conjecture of Birch and Swinnerton-Dyer, V. Kolyvagin [The Grothendieck Festschrift, Vol. II, Prog. Math. 87, 435-483 (1990; Zbl 0742.14017)] introduced the concept of an Euler system. Loosely speaking, an Euler system is a set of points on an algebraic group satisfying two conditions: a norm property and a congruence property. In the present paper, the author shows that the norm property implies a weak form of the congruence property that is sufficient for most applications. The proof is fairly formal, relying on the introduction of a “universal Euler system”.The main importance of the result is that the units predicted to exist by Stark’s conjecture satisfy the norm condition, hence the congruence condition, so they conjecturally yield a new family of Euler systems, which can be used to study the structure of ideal class groups as in the work of F. Thaine [Ann. Math., II. Ser. 128, 1-18 (1988; Zbl 0665.12003)], the author [Invent. Math. 89, 511-526 (1987; Zbl 0628.12007)], and V. Kolyvagin. Reviewer: L.Washington (College Park) Cited in 2 ReviewsCited in 13 Documents MSC: 11R27 Units and factorization 11G16 Elliptic and modular units 11R29 Class numbers, class groups, discriminants 14G05 Rational points Keywords:Euler system; norm property; congruence property; units; Stark’s conjecture; ideal class groups Citations:Zbl 0742.14017; Zbl 0665.12003; Zbl 0628.12007 PDFBibTeX XMLCite \textit{K. Rubin}, J. Reine Angew. Math. 425, 141--154 (1992; Zbl 0752.11045) Full Text: DOI Crelle EuDML