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Showing 1 to 3 of 3 for “"Modular curves"”.
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Comparison of Integral Structures on the Space of Modular Forms of Full Level N
… different integral structures on the space of modular forms over the rationals Q, one coming from arithmetic via q-expansions, the other coming from geometry via integral models of modular curves. Both structures are stable under the Hecke operators; furthermore, their quotient is finite …
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Explicit moduli spaces for curves of genus 1 and 2
… thesis we study pairs of $N$-congruent elliptic curves. That is, we study pairs of elliptic curves whose $N$-torsion subgroups are isomorphic as Galois modules. In particular, we study the moduli surfaces $Z_{N,r}$ which parametrise $N$-congruences of elliptic curves which raise the Weil pairing …
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p-adic Heights of Heegner points on Shimura curves
Let f be a primitive Hilbert modular form of weight 2 and level N for the totally real field F, and let p be an odd rational prime such that f is ordinary at all primes dividing p. When E is a CM extension of F of relative discriminant prime to Np, we give an explicit construction of the p-adic …