منابع مشابه
Jacobians with Complex Multiplication
We construct and study two series of curves whose Jacobians admit complex multiplication. The curves arise as quotients of Galois coverings of the projective line with Galois group metacyclic groups Gq,3 of order 3q with q ≡ 1 mod 3 an odd prime, and Gm of order 2 . The complex multiplications arise as quotients of double coset algebras of the Galois groups of these coverings. We work out the C...
متن کاملHyperelliptic Jacobians without Complex Multiplication
has only trivial endomorphisms over an algebraic closure of the ground field K if the Galois group Gal(f) of the polynomial f ∈ K[x] is “very big”. More precisely, if f is a polynomial of degree n ≥ 5 and Gal(f) is either the symmetric group Sn or the alternating group An then End(J(C)) = Z. Notice that it easily follows that the ring of K-endomorphisms of J(C) coincides with Z and the real pro...
متن کاملOrbifold points on Teichmüller curves and Jacobians with complex multiplication
For each integer D ≥ 5 with D ≡ 0 or 1 mod 4, the Weierstrass curve WD is an algebraic curve and a finite volume hyperbolic orbifold which admits an algebraic and isometric immersion into the moduli space of genus two Riemann surfaces. The Weierstrass curves are the main examples of Teichmüller curves in genus two. The primary goal of this paper is to determine the number and type of orbifold p...
متن کاملHyperelliptic Jacobians with Real Multiplication
Let K be a field of characteristic different from 2, and let f(x) be a sextic polynomial irreducible over K with no repeated roots, whose Galois group is A5. If the Jacobian of the hyperelliptic curve y = f(x) admits real multiplication over the ground field from an order of a real quadratic number field, then either its endomorphism algebra is this quadratic field or the Jacobian is supersingu...
متن کاملHyperelliptic Jacobians without Complex Multiplication in Positive Characteristic
has only trivial endomorphisms over an algebraic closure of the ground field K if the Galois group Gal(f) of the polynomial f ∈ K[x] of even degree is “very big”. More precisely, if f is a polynomial of even degree n ≥ 10 and Gal(f) is either the symmetric group Sn or the alternating group An then End(J(C)) = Z. Notice that it is known [10] that in this case (and even for all integers n ≥ 5) ei...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2011
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2011-05560-1