Аннотация:
Following ideas of Katz, Kontsevich, and Nori, we construct a tannakian category of “exponential motives” over a subfield $k$ of the complex numbers by applying Nori's formalism to rapid decay cohomology, which one thinks of as the Betti realisation. This category of exponential motives contains the classical mixed motives à la Nori. We then introduce the de Rham realisation, as well as a comparison isomorphism with the Betti realisation. When $k=Q$, this comparison isomorphism yields a class of complex numbers, "exponential periods", which includes special values of the gamma and the Bessel functions, the Euler–Mascheroni constant, and other interesting numbers which are not expected to be periods of classical motives. In particular, we attach to exponential motives a Galois group which conjecturally governs all algebraic relations among their periods.
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