Year: 2025
Type: preprint
Abstract: Descent theory (a modern formulation of Fermat's classical method of infinite descent) is a powerful tool in arithmetic geometry. In this article, we reinterpret descent theory through the lens of quotient stacks and apply it in the setting where it first arose: the Diophantine study of generalized Fermat equations (1) \[ Ax^a + By^b + Cz^c = 0. \] We focus on understanding the arithmetic of the stacks that arise from the study of primitive integral solutions to general Fermat equations, rather than on solving any particular instance of the equation.
Source: arXiv (Cornell University)
Author: Arango-Piñeros, Santiago
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414525010
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