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Mosc. Math. J., 2004, Volume 4, Number 1, Pages 217–244 (Mi mmj149)  

This article is cited in 50 scientific papers (total in 50 papers)

Varieties over field with one element

Ch. Soulé

Institut des Hautes Études Scientifiques

Abstract: We propose a definition of varieties over “the field with one element”, a notion which had been imagined by Tits, Manin and others. Such a variety has an extension to the integers which is a usual algebraic variety. Examples include smooth toric varieties and euclidean lattices. We also define and compute a zeta function for these objects, and we propose a motivic interpretation of the image of Adams $J$-homomorphism.

Key words and phrases: Algebraic varieties, toric varieties, euclidean lattices, zeta functions, $J$-homomorphism.


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MSC: 14A99, 14M25, 11M99, 55Q50
Received: May 6, 2003; in revised form August 28, 2003

Citation: Ch. Soulé, “Varieties over field with one element”, Mosc. Math. J., 4:1 (2004), 217–244

Citation in format AMSBIB
\by Ch.~Soul\'e
\paper Varieties over field with one element
\jour Mosc. Math.~J.
\yr 2004
\vol 4
\issue 1
\pages 217--244

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    This publication is cited in the following articles:
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    37. Lo Catharine Wing Kwan, Marcolli M., “F-Zeta-Geometry, Tate Motives, and the Habiro Ring”, Int. J. Number Theory, 11:2 (2015), 311–339  crossref  mathscinet  zmath  isi  scopus
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