Explicit non-trivial elements in K_4^{(3)} of Fermat curves are built uniformly in N, with regulators expressed via Zagier's trilogarithm and hypergeometric functions, plus numerical checks of Beilinson conjectures for N=3,4,6.
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Proves explicit reciprocity law for Euler system of spin motive of genus 2 Siegel modular form, giving partial Iwasawa Main Conjecture and Bloch-Kato conjecture results.
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Elements in $K_4$ and regulator maps of Fermat curves
Explicit non-trivial elements in K_4^{(3)} of Fermat curves are built uniformly in N, with regulators expressed via Zagier's trilogarithm and hypergeometric functions, plus numerical checks of Beilinson conjectures for N=3,4,6.
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On the Bloch-Kato conjecture for GSp(4)
Proves explicit reciprocity law for Euler system of spin motive of genus 2 Siegel modular form, giving partial Iwasawa Main Conjecture and Bloch-Kato conjecture results.