#### DOCUMENTA MATHEMATICA, Vol. 6 (2001), 69-97

C. Deninger

On the Gamma-Factors of Motives II

Using an idea of C. Simpson we describe Serre's local $\Gamma$-factors in terms of a complex of sheaves on a simple dynamical system. This geometrizes our earlier construction of the $\Gamma$-factors. Relations of this approach with the $\varepsilon$-factors are also studied.

2000 Mathematics Subject Classification: 11G40, 14Fxx, 14G10, 14G40

Keywords and Phrases: $\Gamma$-factors, motives, non-abelian Hodge theory, $\varepsilon$-factors, explicit formulas, Rees bundle, dynamical systems

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