Bounding generators for the kernel and cokernel of the tame symbol for curves
Rob de Jeu

TL;DR
This paper establishes bounds on generators for the kernel and cokernel of the tame symbol on algebraic curves, with potential applications to Chow groups, based on the curve's arithmetic genus.
Contribution
It provides explicit bounds for generators of the tame symbol's kernel and cokernel on curves, a novel result linking algebraic geometry and arithmetic invariants.
Findings
Bounds depend on the arithmetic genus of the curve
Explicit bounds for the cokernel's generators
Potential application to Chow groups
Abstract
Let be a regular, irreducible curve that is projective over a field. We obtain bounds in terms of the arithmetic genus of for the generators that are required for the cokernel of the tame symbol, as well as, under a simplifying assumption, its kernel. We briefly discuss a potential application to Chow groups.
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Taxonomy
TopicsAdvanced Steganography and Watermarking Techniques · Chaos-based Image/Signal Encryption · Robotic Path Planning Algorithms
