تقرير
Etale descent obstruction and anabelian geometry of curves over finite fields
العنوان: | Etale descent obstruction and anabelian geometry of curves over finite fields |
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المؤلفون: | Creutz, Brendan, Voloch, Jose Felipe |
المصدر: | \'Epijournal de G\'eom\'etrie Alg\'ebrique, volume 8 (2024), Article no 10 |
سنة النشر: | 2023 |
المجموعة: | Mathematics |
مصطلحات موضوعية: | Mathematics - Number Theory, Mathematics - Algebraic Geometry, 11G20, 11G30, 14G05, 14G15 |
الوصف: | Let $C$ and $D$ be smooth, proper and geometrically integral curves over a finite field $F$. Any morphism from $D$ to $C$ induces a morphism of their \'etale fundamental groups. The anabelian philosophy proposed by Grothendieck suggests that, when $C$ has genus at least $2$, all open homomorphisms between the \'etale fundamental groups should arise in this way from a nonconstant morphism of curves. We relate this expectation to the arithmetic of the curve $C_K$ over the global function field $K = F(D)$. Specifically, we show that there is a bijection between the set of conjugacy classes of well-behaved morphism of fundamental groups and locally constant adelic points of $C_K$ that survive \'etale descent. We use this to provide further evidence for the anabelian conjecture by relating it to another recent conjecture by Sutherland and the second author. |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2306.04844 |
رقم الأكسشن: | edsarx.2306.04844 |
قاعدة البيانات: | arXiv |
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