Geodesic
Families of coherent PEL automorphic forms
Documenta mathematica, Tome 27 (2022), pp. 213-294.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

In this article we give a construction of eigenvarieties by geometrically interpolating coherent automorphic sheaves of (PEL) Shimura varieties and their global sections. The new feature is that we particularly study the case of an empty ordinary locus, and thus use a replacement of the canonical subgroup in this situation. We specifically take into account the case of small primes and use this particular construction at a specific endoscopic point to prove new cases of the Bloch-Kato conjecture for characters of an imaginary quadratic field.
Classification : 14G35, 11G18, 11F33, 14K10, 11F55, 11G40, 14L05, 14G22
Keywords: automorphic forms, Shimura varieties, eigenvarieties, Bloch-Kato conjecture, \(p\)-divisible groups 
@article{DOCMA_2022__27__a61,
     author = {Hernandez, Valentin},
     title = {Families of coherent {PEL} automorphic forms},
     journal = {Documenta mathematica},
     pages = {213--294},
     publisher = {mathdoc},
     volume = {27},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a61/}
}
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Hernandez, Valentin. Families of coherent PEL automorphic forms. Documenta mathematica, Tome 27 (2022), pp. 213-294. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a61/