Using the Chenevier-Lannes classification of automorphic representations and a conjectural correspondence to ℓ-adic Galois representations, the Euler characteristics of overline M_{3,n} and M_{3,n} (n≤14) and of local systems V_λ on A_3 (|λ|≤16) are computed in the Grothendieck group of such Galois/
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An expository introduction to intersection theory on the moduli space of curves, covering the tautological ring and methods to determine generation of the Chow ring by tautological classes.
Expository survey of when Chow rings and cohomology rings of moduli spaces of curves are tautological and when their point counts over finite fields are polynomials in q.
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Cohomology of moduli spaces via a result of Chenevier and Lannes
Using the Chenevier-Lannes classification of automorphic representations and a conjectural correspondence to ℓ-adic Galois representations, the Euler characteristics of overline M_{3,n} and M_{3,n} (n≤14) and of local systems V_λ on A_3 (|λ|≤16) are computed in the Grothendieck group of such Galois/