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2 results

  • On higher regulators of Siegel threefolds II: the connection to the special value

  • Part of
  • Francesco Lemma
  • Journal:
    Compositio Mathematica / Volume 153 / Issue 5 / May 2017
    Published online by Cambridge University Press:
    27 March 2017, pp. 889-946
    Print publication:
    May 2017
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  • We establish a connection between motivic cohomology classes over the Siegel threefold and non-critical special values of the degree-four $L$-function of some cuspidal automorphic representations of $\text{GSp}(4)$. Our computation relies on our previous work [On higher regulators of Siegel threefolds I: the vanishing on the boundary, Asian J. Math. 19 (2015), 83–120] and on an integral representation of the $L$-function due to Piatetski-Shapiro.

  • Geometric Euler systems for locally isotropic motives

  • Tom Weston
  • Journal:
    Compositio Mathematica / Volume 140 / Issue 2 / March 2004
    Published online by Cambridge University Press:
    04 December 2007, pp. 317-332
    Print publication:
    March 2004
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  • In this paper, we construct a theory of geometric Euler systems, complementary to the arithmetic theory of Rubin, Kato and Perrin-Riou. We show that geometric Euler systems can be used to prove the finiteness of certain Galois representations of weight zero and we discuss a conjectural framework for the existence of geometric Euler systems for motivic Galois representations. We give applications to adjoint Selmer groups of certain classical and Drinfeld modular forms.