We construct a Euler system in the cohomology of the tensor product of the Galois representations attached to two modular forms, using elements in the higher Chow groups of products of modular curves. We use these elements to prove a finiteness theorem for the strict Selmer group of the Galois representation when the associated $p$-adic Rankin–Selberg $L$-function is nonvanishing at $s = 1$.
Antonio Lei 1 ; David Loeffler 2 ; Sarah Livia Zerbes 3
@article{10_4007_annals_2014_180_2_6,
author = {Antonio Lei and David Loeffler and Sarah Livia Zerbes},
title = {Euler systems for {Rankin{\textendash}Selberg} convolutions of modular forms},
journal = {Annals of mathematics},
pages = {653--771},
year = {2014},
volume = {180},
number = {2},
doi = {10.4007/annals.2014.180.2.6},
mrnumber = {3224721},
zbl = {1315.11044},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2014.180.2.6/}
}
TY - JOUR AU - Antonio Lei AU - David Loeffler AU - Sarah Livia Zerbes TI - Euler systems for Rankin–Selberg convolutions of modular forms JO - Annals of mathematics PY - 2014 SP - 653 EP - 771 VL - 180 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2014.180.2.6/ DO - 10.4007/annals.2014.180.2.6 LA - en ID - 10_4007_annals_2014_180_2_6 ER -
%0 Journal Article %A Antonio Lei %A David Loeffler %A Sarah Livia Zerbes %T Euler systems for Rankin–Selberg convolutions of modular forms %J Annals of mathematics %D 2014 %P 653-771 %V 180 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2014.180.2.6/ %R 10.4007/annals.2014.180.2.6 %G en %F 10_4007_annals_2014_180_2_6
Antonio Lei; David Loeffler; Sarah Livia Zerbes. Euler systems for Rankin–Selberg convolutions of modular forms. Annals of mathematics, Tome 180 (2014) no. 2, pp. 653-771. doi: 10.4007/annals.2014.180.2.6
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