Galois representations associated to Siegel modular forms of low weight. (English) Zbl 0810.11033

Taylor, Richard

Duke Math. J. 63, No. 2, 281-332 (1991).

The main result of the paper is the existence of Galois representations associated to certain genus 2 Siegel modular forms of low weight. The proof uses the already known (Shimura, Deligne, Faltings-Chai) analogous result for sufficiently high weight and congruences with systems of Hecke eigenvalues of form of high weight. The notion of pseudorepresentation is defined and used as a tool to construct the \(\lambda\)-adic representations from sufficiently many congruences. An important application of the main result is given in the last section. There it is shown how to eliminate one of the two hypotheses needed in the construction of Galois representations associated to certain Maass forms by Blasius and Ramakrishnan.

MSC:

11F46	Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
11F80	Galois representations
11R39	Langlands-Weil conjectures, nonabelian class field theory
14G35	Modular and Shimura varieties

Keywords:

existence of Galois representations; Siegel modular forms; congruences; systems of Hecke eigenvalues; pseudorepresentation; Maass forms

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