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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 polylogarithmic complexes of weight 3 defined by Goncharov and De Jeu. The construction is uniform in the level and uses new modular units obtained as cross-ratios of division values of the Weierstrass P function. These units provide explicit triangulations of the 3-term relations in K_2 of modular curves, which in turn give rise to elements in K_4. Based on numerical computations and on recent results of W. 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 Connect in order to contact the contributor
Submitted on : Thursday, September 22, 2022 - 11:35:50 PM
Last modification on : Friday, September 30, 2022 - 4:02:14 AM

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François Brunault. On the K_4 group of modular curves. {date}. ⟨ensl-03012466v2⟩

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