Geodesic
Automorphism groups of fields, and their representations
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 62 (2007) no. 6, pp. 1121-1186

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This article contains a study of the automorphism group $G$ of an extension $F|k$ of an algebraically closed field, and of smooth linear and semilinear representations of $G$. It is explained how the representation theory of $G$ is connected with birational geometry, algebraic cycles, motives, and other geometric questions. 
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     author = {M. Z. Rovinskii},
     title = {Automorphism groups of fields, and their representations},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     language = {en},
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M. Z. Rovinskii. Automorphism groups of fields, and their representations. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 62 (2007) no. 6, pp. 1121-1186. http://geodesic.mathdoc.fr/item/RM_2007_62_6_a1/