On the $K_4$ group of modular curves
| Autor: | Brunault, François |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $\wp$ 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. Comment: Revised version. Sections 5, 6, 8 and 9 have been expanded, and links to PARI/GP scripts have been added. Several points have been corrected or clarified |
| Databáze: | arXiv |
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