291 citations
- Massachusetts Institute of TechnologyUS4 papers
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- Brookhaven National LaboratoryUS2 papers
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- Tata Institute of Fundamental ResearchIN2 papers
6 papers · 1 filter
Ihara's lemma for imaginary quadratic fields
Krzysztof Klosin
An analogue over imaginary quadratic fields of a result in algebraic number theory known as Ihara's lemma is established. More precisely, we show that for a prime ideal P of the ri…
Open conditions for infinite multiplicity eigenvalues on elliptic curves
Bo-Hae Im, Michael Larsen
Let E be an elliptic curve defined over a number field K, V the complexification of the group of rational points of E over an algebraic closure L of K, and G the Galois group Gal(L…
Weak approximation for linear systems of quadrics
Bo-Hae Im, Michael Larsen
We give local conditions at the infinite places of a number field K ensuring that the intersection of n quadrics in projective N-space over K, N >> n, satisfies weak approximation.
Reduction of homomorphisms mod p and algebraicity
Chandrashekhar Khare, Dipendra Prasad
{Let be a number field, and abelian varieties over . Let (resp. ) be a non-torsion point in (resp. ) such that for almost all places o…
Limits of residually irreducible p-adic Galois representations
Chandrashekhar Khare
In this note we produce examples of converging sequences of Galois representations, and study some of their properties. Some of the results here are used in the preprint math.NT/02…
F-split Galois representations are potentially abelian
Chandrashekhar Khare
In this note we relate the property of a semisimple l-adic Galois representation being "F-split" for a number field F to its having abelian image. By F-split we mean that the chara…