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On the K_4 group of modular curves

Abstract : We construct elements in the group K_4 of modular curves using the polylog-arithmic complexes of weight 3 defined by Goncharov and de Jeu. The construction is uniform in the level and makes use of new modular units obtained as cross-ratios of division values of the Weierstraß P-function. These units provide explicit triangulations of the Manin 3-term relations in K_2 of modular curves, which in turn gives rise to elements in K_4. Based on numerical computations and on recent results of Weijia Wang, we conjecture that these elements are proportional to the Beilinson elements defined using the Eisenstein symbol.
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-03012466
Contributor : François Brunault <>
Submitted on : Wednesday, November 18, 2020 - 3:32:55 PM
Last modification on : Friday, November 20, 2020 - 3:23:20 AM

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  • HAL Id : ensl-03012466, version 1

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François Brunault. On the K_4 group of modular curves. 2020. ⟨ensl-03012466⟩

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