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The Universal Kolyvagin Recursion Implies the Kolyvagin Recursion

Yi Ouyang

Acta Mathematica Sinica, English Series > 2007 > 23 > 7 > 1163-1172

Let $$\mathfrak U_z $$ be the universal norm distribution and M a fixed power of prime p. By using the double complex method employed by Anderson, we study the universal Kolyvagin recursion occurring in the canonical basis in the cohomology group $$H^0(G_z,\;{\mathfrak U}_z/M{\mathfrak U}_z).$$ We furthermore show that the universal Kolyvagin recursion implies the Kolyvagin recursion in...

article

Two-primary algebraic K-theory of two-regular number fields

John Rognes, Paul Arne stvr

Mathematische Zeitschrift > 2000 > 233 > 2 > 251-263

Abstract. We explicitly calculate all the 2-primary higher algebraic K-groups of the rings of integers of all 2-regular quadratic number fields, cyclotomic number fields, or maximal real subfields of such. Here 2-regular means that (2) does not split in the number field, and its narrow Picard group is of odd order.

article

On the ideal class groups of the maximal real subfields of number fields with all roots of unity

Masato Kurihara

Journal of the European Mathematical Society > 1999 > 1 > 1 > 35-49

In this paper, for a totally real number field k we show the ideal class group of k(n0n)+ is trivial. We also study the p-component of the ideal class group of the cyclotomic Zp-extension.

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11R18 (3)
11G99 (1)
11R11 (1)
11R23 (1)
11R29 (1)
11R37 (1)
11R42 (1)
19F27. (1)
EULER SYSTEM (1)
KOLYVAGIN RECURSION (1)
MATHEMATICS SUBJECT CLASSIFICATION (1991): 11R23 (1)
MATHEMATICS SUBJECT CLASSIFICATION (1991): 19D50 (1)
UNIVERSAL DISTRIBUTION (1)
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The Universal Kolyvagin Recursion Implies the Kolyvagin Recursion

Two-primary algebraic K-theory of two-regular number fields

On the ideal class groups of the maximal real subfields of number fields with all roots of unity

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