Twists of Modular Forms and Endomorphisms of Abelian Varieties.
Dividing rational points on abelian varieties of CM-type
-adic -functions attached to characters of -power order
A Modular Construction of Unramified p-Extension of Q (...).
On ...-Adic Representations Attached to Modular Forms.
Mod p Hecke Operators and Congruences Between Modular Forms.
Sur la recherche des -extensions non ramifiées de
On the equation
We discuss the equation in which a, b, and c are non-zero relatively prime integers, p is an odd prime number, and α is a positive integer. The technique used to prove Fermat’s Last Theorem shows that the equation has no solutions with α < 1 or b even. When α=1 and b is odd, there are the two trivial solutions (±1, ∓ 1, ±1). In 1952, Dénes conjectured that these are the only ones. Using methods of Darmon, we prove this conjecture for p≡ 1 mod 4.
From the Taniyama-Shimura conjecture to Fermat's last theorem
Wiles dokázal Taniyamovu hypotézu; důsledkem je Fermatova věta
Values of Abelian L-functions at Negative Integers over Totally Real Fields.
Galois theory and torsion points on curves
In this paper, we survey some Galois-theoretic techniques for studying torsion points on curves. In particular, we give new proofs of some results of A. Tamagawa and the present authors for studying torsion points on curves with “ordinary good” or “ordinary semistable” reduction at a given prime. We also give new proofs of : (1) the Manin-Mumford conjecture : there are only finitely many torsion points lying on a curve of genus at least embedded in its jacobian by an Albanese map; and (2) the...
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