Two-dimensional $l$-adic representations of the Galois group of a global field of characteristic $p$ and automorphic forms on $GL(2)$
Zapiski Nauchnykh Seminarov POMI, Automorphic functions and number theory. Part II, Tome 134 (1984), pp. 138-156
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It is known that to each cuspidal automorphic representation of $GL(2)$ over the adele ring of a global field $k$ of characteristic $p$ there corresponds an irreducible two-dimensional $l$-adic representation of the Galois group of $k$. In the present paper it is proved that to each irreducible two-dimensional $l$-adic representation of the Galois group there corresponds a cuspical automorphic representation of $GL(2)$ over the adele ring. Thus the proof of the Langlands conjecture for $GL(2,k)$ is completed.
@article{ZNSL_1984_134_a6,
author = {V. G. Drinfeld},
title = {Two-dimensional $l$-adic representations of the {Galois} group of a~global field of characteristic~$p$ and automorphic forms on $GL(2)$},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {138--156},
year = {1984},
volume = {134},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_134_a6/}
}
TY - JOUR AU - V. G. Drinfeld TI - Two-dimensional $l$-adic representations of the Galois group of a global field of characteristic $p$ and automorphic forms on $GL(2)$ JO - Zapiski Nauchnykh Seminarov POMI PY - 1984 SP - 138 EP - 156 VL - 134 UR - http://geodesic.mathdoc.fr/item/ZNSL_1984_134_a6/ LA - ru ID - ZNSL_1984_134_a6 ER -
%0 Journal Article %A V. G. Drinfeld %T Two-dimensional $l$-adic representations of the Galois group of a global field of characteristic $p$ and automorphic forms on $GL(2)$ %J Zapiski Nauchnykh Seminarov POMI %D 1984 %P 138-156 %V 134 %U http://geodesic.mathdoc.fr/item/ZNSL_1984_134_a6/ %G ru %F ZNSL_1984_134_a6
V. G. Drinfeld. Two-dimensional $l$-adic representations of the Galois group of a global field of characteristic $p$ and automorphic forms on $GL(2)$. Zapiski Nauchnykh Seminarov POMI, Automorphic functions and number theory. Part II, Tome 134 (1984), pp. 138-156. http://geodesic.mathdoc.fr/item/ZNSL_1984_134_a6/