Search results for "Tate conjecture"

showing 2 items of 2 documents

On the number of prime divisors of the order of elliptic curves modulo p

2005

CombinatoricsDiscrete mathematicsAlgebra and Number TheorySato–Tate conjectureCounting points on elliptic curvesSchoof's algorithmTwists of curvesSupersingular elliptic curveLenstra elliptic curve factorizationPrime (order theory)Division polynomialsMathematicsActa Arithmetica
researchProduct

Modular Calabi-Yau threefolds of level eight

2005

In the studies on the modularity conjecture for rigid Calabi-Yau threefolds several examples with the unique level 8 cusp form were constructed. According to the Tate Conjecture correspondences inducing isomorphisms on the middle cohomologies should exist between these varieties. In the paper we construct several examples of such correspondences. In the constructions elliptic fibrations play a crucial role. In fact we show that all but three examples are in some sense built upon two modular curves from the Beauville list.

Pure mathematicsConjectureMathematics - Number Theory14G1014J32General MathematicsModular formModular invariancemodular forms14G10; 14J32Cusp formModular curveAlgebraMathematics - Algebraic GeometryMathematics::Algebraic GeometryModular elliptic curveCalabi-YauFOS: MathematicsCalabi–Yau manifoldNumber Theory (math.NT)Tate conjectureAlgebraic Geometry (math.AG)MathematicsTate conjecturedouble coverings
researchProduct