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Independence of ℓ for Frobenius conjugacy classes attached to abelian varieties
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DOI：10.4007/annals.2025.202.3.3.png)
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Abstract
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Let A be an abelian variety over a number field E subset of C, and let G denote the Mumford-Tate group of A. After replacing E by a finite extension, the action of the absolute Galois group Gal(E/E) on the & ell;-adic cohomology H1et(AE, Q & ell;) factors through G(Q & ell;). We show that for v an odd prime of E where A has good reduction, the conjugacy class of Frobenius Frobvin G(Q & ell;) is independent of & ell;. Along the way, we prove that under certain hypotheses, every point in the mu -ordinary locus of the special fiber of Shimura varieties has a special point lifting it.
Keywords:
Abelian varieties
Mumford-Tate group
Shimura varieties
& ell
-independence
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