Weil bounds for singular curves

DOI10.1007/BF01195534zbMath0877.11038MaRDI QIDQ1919700

Eric Bach

Publication date: 10 October 1996

Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)

zbMATH Keywords

finite fieldWeil boundsingular curvesarithmetic genusnumber of rational pointssmooth irreducible curve

Mathematics Subject Classification ID

Curves over finite and local fields (11G20) Singularities of curves, local rings (14H20)

Related Items (5)

On the characteristic polynomials of the Frobenius endomorphism for projective curves over finite fields ⋮ A new perspective on the powers of two descent for discrete logarithms in finite fields ⋮ Counting curves and their projections ⋮ Carlitz-Wan conjecture for permutation polynomials and Weil bound for curves over finite fields ⋮ Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic

Cites Work

• Toward a theory of Pollard's rho method
• On the number of points on a complete intersection over a finite field. (Appendix: Number of points on singular complete intersections by Nicholas M. Katz)
• On a theorem of Castelnuovo, and the equations defining space curves
• Invariants of analytic \({\mathbb{Z}}_ 2\)-manifolds
• The number of points on a singular curve over a finite field
• Realistic analysis of some randomized algorithms
• Equivalence relations on algebraic curves
• On the arithmetic genera and the effective genera of algebraic curves
• THE GENUS OF AN ALGEBRAIC CURVE
• The number of points on certain algebraic curves over finite fields
• Complete Intersections and Connectedness
• An Arithmetic Theory of Adjoint Plane Curves
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