Abhyankar's Conjecture

For a Finite Group , let be the Subgroup generated by all the Sylowp-Subgroup of . If is a projective curve in characteristic , and if , ..., are points of (for ), then a Necessary and Sufficient condition that occur as the Galois Group of a finitecovering of , branched only at the points , ..., , is that the Quotient Group has generators.

Raynaud (1994) solved the Abhyankar problem in the crucial case of the affine line (i.e., the projective line with a pointdeleted), and Harbater (1994) proved the full Abhyankar conjecture by building upon this special solution.

References

Abhyankar, S. ``Coverings of Algebraic Curves.'' Amer. J. Math. 79, 825-856, 1957.

Harbater, D. ``Abhyankar's Conjecture on Galois Groups Over Curves.'' Invent. Math. 117, 1-25, 1994.

Raynaud, M. ``Revêtements de la droite affine en caractéristique et conjecture d'Abhyankar.'' Invent. Math. 116, 425-462, 1994.

• de la Loubere's Method
• Delannoy Number
• Delaunay Triangulation
• Delian Constant
• Delian Problem
• de Longchamps Point
• Del Pezzo Surface
• Delta Amplitude
• Delta Curve
• Delta Function
• Deltahedron
• Delta Sequence
• Delta Variation
• Deltoid
• Deltoidal Hexecontahedron
• Deltoidal Icositetrahedron
• Deltoid Caustic
• Deltoid Evolute
• Deltoid Involute
• Deltoid Pedal Curve
• Deltoid Radial Curve
• de Mere's Problem
• Demlo Number
• de Moivre-Laplace Theorem
• de Moivre Number