Finding Large Selmer Rank via an Arithmetic Theory of Local Constants

DSpace/Manakin Repository

Finding Large Selmer Rank via an Arithmetic Theory of Local Constants

Citable link to this page

 

 
Title: Finding Large Selmer Rank via an Arithmetic Theory of Local Constants
Author: Mazur, Barry C.; Rubin, Karl

Note: Order does not necessarily reflect citation order of authors.

Citation: Mazur, Barry C., and Karl Rubin. 2007. Finding large Selmer rank via an arithmetic theory of local constants. Annals of Mathematics 166(2): 579-612.
Access Status: Full text of the requested work is not available in DASH at this time (“dark deposit”). For more information on dark deposits, see our FAQ.
Full Text & Related Files:
Abstract: We obtain lower bounds for Selmer ranks of elliptic curves over dihedral extensions of number fields. Suppose \(K∕k\) is a quadratic extension of number fields, \(E\) is an elliptic curve defined over k,and p is an odd prime. Let \(K−\) denote the maximal abelian p-extension of \(K\) that is unramified at all primes where E has bad reduction and that is Galois over \(k\) with dihedral Galois group (i.e., the generator c of Gal\((K∕k)\) acts on \(Gal(K−∕K)\) by inversion). We prove (under mild hypotheses on \(p\)) that if the \(Zp\)-rank of the pro-\(p\) Selmer group \(S_p(E∕K)\) is odd, then \(rankZ_p S_p(E∕F) \ge [F : K]\) for every finite extension \(F\) of \(K\) in \(K−\).
Published Version: doi:10.4007/annals.2007.166.579
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:10355839
Downloads of this work:

Show full Dublin Core record

This item appears in the following Collection(s)

 
 

Search DASH


Advanced Search
 
 

Submitters