Some remarks on the companions conjecture for normal varieties
Number Theory
2025-04-14 v1 Algebraic Geometry
Abstract
Drinfeld in 2010 proved the companions conjecture for smooth varieties over a finite field, generalizing L. Lafforgue's result for smooth curves. We study the obstruction to prove the conjecture for arbitrary normal varieties. To do this, we introduce a new property of morphisms. We verify this property in some cases, showing thereby the companions conjecture for some singular normal varieties.
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Cite
@article{arxiv.2006.09954,
title = {Some remarks on the companions conjecture for normal varieties},
author = {Marco D'Addezio},
journal= {arXiv preprint arXiv:2006.09954},
year = {2025}
}
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8 pages