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Diophantine stability | | Barry Mazur
; Karl Rubin
; with an appendix by Michael Larsen
; | | Date: |
16 Mar 2015 | | Abstract: | If $V$ is an irreducible algebraic variety over $K$, and $L$ is a field
containing $K$, we say that $V$ is diophantine-stable for $L/K$ if $V(L) =
V(K)$. We prove that if $V$ is either a simple abelian variety, or a curve of
genus at least one, then under mild hypotheses there is a set $S$ of rational
primes with positive density such that for every $ell in S$ and every $n ge
1$, there are infinitely many cyclic extensions $L/K$ of degree $ell^n$ for
which $V$ is diophantine-stable. We use this result to study the collection of
finite extensions of $K$ generated by points in $V(ar{K})$. | | Source: | arXiv, 1503.4642 | | Services: | Forum | Review | PDF | Favorites | |
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