21 citations · 27 across the 7 of their papers we have counts for
7 papers
Class groups of real cyclotomic fields
Mohit Mishra, Rene Schoof, Lawrence C. Washington
We prove that every finite abelian group G occurs as a subgroup of the class group of infinitely many real cyclotomic fields.
Class group of real cyclotomic fields
Mohit Mishra
In this article, we prove that every finite abelian group of odd order occurs as a subgroup of the class group of infinitely many real cyclotomic fields.
Visibility of ideal classes
Rene Schoof, Lawrence C. Washington
Cremona, Mazur, and others have studied what they call visibility of elements of Shafarevich-Tate groups of elliptic curves. The analogue for an abelian number field is capitul…
Four primality testing algorithms
Rene Schoof
In this expository paper we describe four primality tests. The first test is very efficient, but is only capable of proving that a given number is either composite or 'very probabl…
Abelian varieties over Q with bad reduction in one prime only
Rene' Schoof
Let l be a prime. We show that there do not exist any non-zero semi-stable abelian varieties over Q with good reduction outside l if and only if l=2, 3, 5, 7 or 13. We show that an…
A refined counter-example to the support conjecture for abelian varieties
Michael Larsen, René Schoof
If A/K is an abelian variety over a number field and P and Q are rational points, the original support conjecture asserted that if the order of Q (mod p) divides the order of P (mo…