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Invariants, Shimura Variety, and Hecke Algebra

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Elliptic Curves and Arithmetic Invariants

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Abstract

In the first chapter, we gave an introductory sketch of a proof of nonvanishing modulo p of Dirichlet L-values. Since we have described basics of elliptic curves in an elementary manner in Chap.2, at least we could illustrate our main objectives in this book with a rough outline of their proofs. Detailed proofs (for some of them) will be given after we become equipped with a scheme-theoretic description of elliptic curves and their moduli as the simplest example of Shimura varieties in the following chapters. For some others, we give full proofs here, possibly assuming simplifying assumptions (and we refer to quoted research articles about the author’s proofs in more general cases).

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  1. Department of Mathematics, University of California, Los Angeles, CA, USA

    Haruzo Hida

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Hida, H. (2013). Invariants, Shimura Variety, and Hecke Algebra. In: Elliptic Curves and Arithmetic Invariants. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6657-4_3

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