Geodesic
THE IWASAWA MAIN CONJECTURE FOR HILBERT MODULAR FORMS
Forum of Mathematics, Sigma, Tome 3 (2015)

Voir la notice de l'article provenant de la source Cambridge University Press

Following the ideas and methods of a recent work of Skinner and Urban, we prove the one divisibility of the Iwasawa main conjecture for nearly ordinary Hilbert modular forms under certain local hypotheses. As a consequence, we prove that for a Hilbert modular form of parallel weight, trivial character, and good ordinary reduction at all primes dividing $p$, if the central critical $L$-value is zero then the $p$-adic Selmer group of it has rank at least one. We also prove that one of the local assumptions in the main result of Skinner and Urban can be removed by a base-change trick. 
@article{10_1017_fms_2015_16,
     author = {XIN WAN},
     title = {THE {IWASAWA} {MAIN} {CONJECTURE} {FOR} {HILBERT} {MODULAR} {FORMS}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {3},
     year = {2015},
     doi = {10.1017/fms.2015.16},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2015.16/}
}
TY  - JOUR
AU  - XIN WAN
TI  - THE IWASAWA MAIN CONJECTURE FOR HILBERT MODULAR FORMS
JO  - Forum of Mathematics, Sigma
PY  - 2015
VL  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1017/fms.2015.16/
DO  - 10.1017/fms.2015.16
LA  - en
ID  - 10_1017_fms_2015_16
ER  - 
%0 Journal Article
%A XIN WAN
%T THE IWASAWA MAIN CONJECTURE FOR HILBERT MODULAR FORMS
%J Forum of Mathematics, Sigma
%D 2015
%V 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1017/fms.2015.16/
%R 10.1017/fms.2015.16
%G en
%F 10_1017_fms_2015_16
XIN WAN. THE IWASAWA MAIN CONJECTURE FOR HILBERT MODULAR FORMS. Forum of Mathematics, Sigma, Tome 3 (2015). doi: 10.1017/fms.2015.16

Cité par Sources :