Geodesic
Change of Selmer group for big Galois representations and application to normalization
Documenta mathematica, Tome 16 (2011), pp. 885-899
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The goal of this note is to prove, under some assumptions, a formula relating the Selmer groups of isogenous Galois representations. Local and global Euler-Poincaré characteristic formulas are key tools in the proof. With additional hypotheses, we use the isogeny formula to study how the formation of Selmer groups interacts with normalization of the coefficient ring and discuss how a main conjecture for a big Galois representation over a non-normal ring follows from a corresponding conjecture over the normalization.
DOI : 10.4171/dm/354
Classification : 11R23, 11R34
Mots-clés : Iwasawa theory, Galois cohomology, Selmer group 
@article{10_4171_dm_354,
     author = {Trevor Arnold and Koopa Tak-Lun Koo},
     title = {Change of {Selmer} group for big {Galois} representations and application to normalization},
     journal = {Documenta mathematica},
     pages = {885--899},
     year = {2011},
     volume = {16},
     doi = {10.4171/dm/354},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/354/}
}
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Trevor Arnold; Koopa Tak-Lun Koo. Change of Selmer group for big Galois representations and application to normalization. Documenta mathematica, Tome 16 (2011), pp. 885-899. doi: 10.4171/dm/354

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