Ineffective descent of genus one curves
Wouter Zomervrucht
TL;DR
This paper provides an explicit and simplified counterexample demonstrating that etale descent of genus one curves is generally ineffective, confirming Raynaud's 1968 result.
Contribution
It offers a fully explicit and simplified construction of the known non-effectiveness of etale descent for genus one curves.
Findings
Counterexample confirms non-effectiveness of etale descent
Explicit construction simplifies understanding of Raynaud's result
Enhances comprehension of descent problems in algebraic geometry
Abstract
Raynaud proved in 1968 that etale descent of genus one curves is not effective in general. In this paper we provide an alternative, simplified construction of this phenomenon. Our counterexample is fully explicit.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Numerical Analysis Techniques · Digital Image Processing Techniques