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Moduli Operad over F_1

Manin, Yuri I. and Marcolli, Matilde (2016) Moduli Operad over F_1. In: Absolute arithmetic and F1-geometry. European Mathematical Society , Zürich, pp. 331-361. ISBN 978-3-03719-157-6.

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In this paper we answer a question raised in [25], Sec. 4, by showing that the genus zero moduli operad {M_(0,n+1)} can be endowed with natural descent data that allow it to be considered as the lift to Spec Z of an operad over F_1. The relevant descent data are based on a notion of constructible sets and constructible functions over F_1, which describes suitable differences of torifications with a positivity condition on the class in the Grothendieck ring. More generally, we do the same for the operads {T_(d,n+1)} (whose components were) introduced in [5]. Finally, we describe a blueprint structure on {M_(0,n)} and we discuss from this perspective the genus zero boundary modular operad {M^0_(g,n+1)}.

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Additional Information:© 2016 EMS Publishing House. The second author acknowledges support and hospitality of the Max Planck Institute and the Mathematical Sciences Research Institute and support from NSF grants DMS-0901221, DMS-1007207, DMS-1201512, PHY-1205440. We thank Paolo Aluffi, Tom Graber and Oliver Lorscheid for constructive criticism, useful comments and discussions.
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Record Number:CaltechAUTHORS:20170712-091753130
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78999
Deposited By: Ruth Sustaita
Deposited On:12 Jul 2017 16:25
Last Modified:03 Oct 2019 18:14

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