Vol. 2, No. 4, 2017

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Rational mixed Tate motivic graphs

Susama Agarwala and Owen Patashnick

Vol. 2 (2017), No. 4, 451–515
Abstract

We study the combinatorics of a subcomplex of the Bloch–Kriz cycle complex that was used to construct the category of mixed Tate motives. The algebraic cycles we consider properly contain the subalgebra of cycles that correspond to multiple logarithms (as defined by Gangl, Goncharov and Levin). We associate an algebra of graphs to our subalgebra of algebraic cycles. We give a purely combinatorial criterion for admissibility. We show that sums of bivalent graphs correspond to coboundary elements of the algebraic cycle complex. Finally, we compute the Hodge realization for an infinite family of algebraic cycles represented by sums of graphs that are not describable in the combinatorial language of Gangl et al.

Keywords
Bloch–Kriz cycle complex, admissible cycles, Hodge realization
Mathematical Subject Classification 2010
Primary: 05C22, 14C15, 57T30
Milestones
Received: 13 May 2016
Revised: 18 October 2016
Accepted: 7 November 2016
Published: 18 July 2017
Authors
Susama Agarwala
Mathematics Department
USNA
Annapolis, MD 21402
United States
Owen Patashnick
School of Mathematics
University of Bristol
Bristol, BS8 1TW
United Kingdom
Heilbronn Institute for Mathematical Research
Bristol
United Kingdom