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On the K_4 group of modular curves

Sur le groupe K_4 des courbes modulaires


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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Dates and versions

ensl-03012466 , version 1 (18-11-2020)
ensl-03012466 , version 2 (22-09-2022)



François Brunault. On the K_4 group of modular curves. 2022. ⟨ensl-03012466v2⟩
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