Papers › On the K₄ group of modular curves
On the K₄ group of modular curves
François Brunault
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We construct elements in the K₄ group of modular curves using the polylogarithmic complexes of weight 3 defined by Goncharov and De Jeu. The construction is uniform in the level and relies on new modular units arising as cross-ratios of division values of the Weierstrass ℘ function. These units provide explicit triangulations of the 3-term relations in K₂, which in turn give rise to elements in K₄. Based on numerical computations and on results of Wang, we conjecture that these elements are proportional to the Beilinson elements defined via Eisenstein symbols.
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