caa a22 4500 378892428 CHVBK 20180305123458.0 cr unu---uuuuu 161128e20041130xx s 000 0 eng 10.1515/crll.2004.2004.577.147 doi (NATIONALLICENCE)gruyter-10.1515/crll.2004.2004.577.147 Dieulefait Luis V. 1. Barcelona. Existence of families of Galois representations and new cases of the Fontaine-Mazur conjecture [Elektronische Daten] [Luis V. Dieulefait] In a previous article, we have proved a result asserting the existence of a compatible family of Galois representations containing a given crystalline irreducible odd two-dimensional representation. We apply this result to establish new cases of the Fontaine-Mazur conjecture, namely, an irreducible Barsotti-Tate λ-adic 2-dimensional Galois representation unramified at 3 and such that the traces ap of the images of Frobenii verify ℚ({a2 p}) = ℚ always comes from an abelian variety. We also show the non-existence of irreducible Barsotti-Tate 2-dimensional Galois representations of conductor 1 and apply this to the irreducibility of Galois representations on level 1 genus 2 Siegel cusp forms. © Walter de Gruyter Grammar, syntax, linguistic structure nationallicence Phonetics, phonology, prosody nationallicence Historical & comparative linguistics nationallicence Journal für die reine und angewandte Mathematik (Crelles Journal) Walter de Gruyter 2004/577(2004-11-30), 147-151 0075-4102 2004:577<147 2004 2004 crll https://doi.org/10.1515/crll.2004.2004.577.147 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/crll.2004.2004.577.147 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Dieulefait Luis V. 1. Barcelona NATIONALLICENCE 773 0- Journal für die reine und angewandte Mathematik (Crelles Journal) Walter de Gruyter 2004/577(2004-11-30), 147-151 0075-4102 2004:577<147 2004 2004 crll CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter