Math @ Duke

Publications [#320426] of Richard Hain
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 Hain, R; Matsumoto, M, Universal Mixed Elliptic Motives,
Journal of the Institute of Mathematics of Jussieu
(December, 2015) [arxiv:1512.03975]
(last updated on 2019/03/25)
Abstract: In this paper we construct a Qlinear tannakian category MEM_1 of universal
mixed elliptic motives over the moduli space M_{1,1} of elliptic curves. It
contains MTM, the category of mixed Tate motives unramified over the integers.
Each object of MEM_1 is an object of MTM endowed with an action of SL_2(Z) that
is compatible with its structure. Universal mixed elliptic motives can be
thought of as motivic local systems over M_{1,1} whose fiber over the
tangential base point d/dq at the cusp is a mixed Tate motive. The basic
structure of the tannakian fundamental group of MEM is determined and the
lowest order terms of all relations are found (using computations of Francis
Brown), including the arithmetic relations, which describe the "infinitesimal
Galois action". We use the presentation to give a new and more conceptual proof
of the IharaTakao congruences.


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