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2017 Rational mixed Tate motivic graphs
Susama Agarwala, Owen Patashnick
Ann. K-Theory 2(4): 451-515 (2017). DOI: 10.2140/akt.2017.2.451


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.


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Susama Agarwala. Owen Patashnick. "Rational mixed Tate motivic graphs." Ann. K-Theory 2 (4) 451 - 515, 2017.


Received: 13 May 2016; Revised: 18 October 2016; Accepted: 7 November 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1368.05062
MathSciNet: MR3681105
Digital Object Identifier: 10.2140/akt.2017.2.451

Primary: 05C22 , 14C15 , 57T30

Keywords: admissible cycles , Bloch–Kriz cycle complex , Hodge realization

Rights: Copyright © 2017 Mathematical Sciences Publishers


Vol.2 • No. 4 • 2017
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