Abstract.
Some of basic properties of the groups of automorphisms of algebraically closed fields and of their smooth representations are studied. In characteristic zero, Grothendieck motives modulo numerical equivalence are identified with a full subcategory in the category of graded smooth representations of certain automorphism groups of algebraically closed fields.
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Supported in part by RFBR grant 02-01-22005
Acknowledgments. I would like to thank Uwe Jannsen for his encouraging interest in this work and many suggestions, and Maxim Kontsevich for a helpful discussion on Proposition 3.22. The present form of Proposition 6.4 is a response to a question posed by Dmitry Kaledin. Several improvements were suggested by the referee. I am grateful to the I.H.E.S. for its hospitality and to the European Post-Doctoral Institute for its support during the period when the prime part of this work was done.
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Rovinsky, M. Motives and admissible representations of automorphism groups of fields. Math. Z. 249, 163–221 (2005). https://doi.org/10.1007/s00209-004-0697-1
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DOI: https://doi.org/10.1007/s00209-004-0697-1