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Lei, Antonio; Loeffler, David; Zerbes, Sarah Livia

Euler systems for modular forms over imaginary quadratic fields. (English) Zbl 1376.11050

Compos. Math. 151, No. 9, 1585-1625 (2015).
Summary: We construct an Euler system attached to a weight 2 modular form twisted by a Grössencharacter of an imaginary quadratic field \(K\), and apply this to bounding Selmer groups.

Cited in 1 Review
Cited in 13 Documents

MSC:

11F85 \(p\)-adic theory, local fields
11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
11G40 \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
14G35 Modular and Shimura varieties

Keywords:

Euler systems; Selmer groups; Rankin-Selberg convolution; Galois representations
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Full Text: DOI arXiv

References:

[1] doi:10.1017/S0017089500006170 · Zbl 0596.10027 · doi:10.1017/S0017089500006170
[3] doi:10.1007/s002080000119 · Zbl 0967.11016 · doi:10.1007/s002080000119
[7] doi:10.1007/s00222-005-0467-7 · Zbl 1093.11065 · doi:10.1007/s00222-005-0467-7
[8] doi:10.1142/S1793042114500699 · Zbl 1314.11066 · doi:10.1142/S1793042114500699
[10] doi:10.4007/annals.2014.180.2.6 · Zbl 1315.11044 · doi:10.4007/annals.2014.180.2.6
[13] doi:10.1007/BF01390166 · Zbl 0349.12006 · doi:10.1007/BF01390166
[15] doi:10.1515/CRELLE.2006.062 · Zbl 1127.11072 · doi:10.1515/CRELLE.2006.062
[16] doi:10.1090/S1056-3911-2014-00670-6 · Zbl 1325.14034 · doi:10.1090/S1056-3911-2014-00670-6
[17] doi:10.1155/IMRN.2005.701 · Zbl 1138.11021 · doi:10.1155/IMRN.2005.701
[18] doi:10.1215/00127094-2142056 · Zbl 1302.11043 · doi:10.1215/00127094-2142056
[19] doi:10.4007/annals.2005.162.1 · Zbl 1093.11037 · doi:10.4007/annals.2005.162.1
[21] doi:10.2307/2118559 · Zbl 0823.11029 · doi:10.2307/2118559
[22] doi:10.1007/s00222-013-0448-1 · Zbl 1301.11074 · doi:10.1007/s00222-013-0448-1
[23] doi:10.1112/jlms/s2-38.1.1 · Zbl 0656.10019 · doi:10.1112/jlms/s2-38.1.1
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