اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA Uniform Field-of-Definition/Field-of-Moduli Bound for Dynamical Systems on $mathbf{P}^N$
65
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let $f:mathbb{P}^Ntomathbb{P}^N$ be an endomorphism of degree $dge2$ defined over $overline{mathbb{Q}}$ or $overline{mathbb{Q}}_p$, and let $K$ be the field of moduli of $f$. We prove that there is a field of definition $L$ for $f$ whose degree $[L:K]$ is bounded solely in terms of $N$ and $d$.
قيم البحث
اقرأ أيضاً
Let Hom^N_d be the set of morphisms of degree d from P^N to itself. For f an element of PGL_{N+1}, let phi^f represent the conjugation action f^{-1} phi f. Let M^N_d = Hom_d^N/PGL_{N+1} be the moduli space of degree d morphisms of P^N. A field of def
inition for class of morphisms is a field over which at least one morphism in the class is defined. The field of moduli for a class of morphisms is the fixed field of the set of Galois elements fixing that class. Every field of definition contains the field of moduli. In this article, we give a sufficient condition for the field of moduli to be a field of definition for morphisms whose stabilizer group is trivial.
A $textit{portrait}$ $mathcal{P}$ on $mathbb{P}^N$ is a pair of finite point sets $Ysubseteq{X}subsetmathbb{P}^N$, a map $Yto X$, and an assignment of weights to the points in $Y$. We construct a parameter space $operatorname{End}_d^N[mathcal{P}]$ wh
ose points correspond to degree $d$ endomorphisms $f:mathbb{P}^Ntomathbb{P}^N$ such that $f:Yto{X}$ is as specified by a portrait $mathcal{P}$, and prove the existence of the GIT quotient moduli space $mathcal{M}_d^N[mathcal{P}]:=operatorname{End}_d^N//operatorname{SL}_{N+1}$ under the $operatorname{SL}_{N+1}$-action $(f,Y,X)^phi=bigl(phi^{-1}circ{f}circphi,phi^{-1}(Y),phi^{-1}(X)bigr)$ relative to an appropriately chosen line bundle. We also investigate the geometry of $mathcal{M}_d^N[mathcal{P}]$ and give two arithmetic applications.
Let us consider an algebraic function field defined over a finite Galois extension $K$ of a perfect field $k$. We give some conditions allowing the descent of the definition field of the algebraic function field from $K$ to $k$. We apply these result
s to the descent of the definition field of a tower of function fields.We give explicitly the equations of the intermediate steps of an Artin-Schreier type extension reduced from $F_{q^2}$ to $F_q$. By applying these results to a completed Garcia-Stichtenoths tower we improve the upper bounds and the upper asymptotic bounds of the bilinear complexity of the multiplication in finite fields.
We establish a structure theorem for the integral points on moduli of special linear rank two local systems over surfaces, using mapping class group descent and boundedness results for systoles of local systems.
We investigate the arithmetic of algebraic curves on coarse moduli spaces for special linear rank two local systems on surfaces with fixed boundary traces. We prove a structure theorem for morphisms from the affine line into the moduli space. We show
that the set of integral points on any nondegenerate algebraic curve on the moduli space can be effectively determined.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
