ترغب بنشر مسار تعليمي؟ اضغط هنا

Isogeny classes and endomorphisms algebras of abelian varieties over finite fields

109   0   0.0 ( 0 )
 نشر من قبل Yuri Zarhin G.
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English
 تأليف Yuri G. Zarhin




اسأل ChatGPT حول البحث

We construct non-isogenous simple ordinary abelian varieties over an algebraic closure of a finite field with isomorphic endomorphism algebras.



قيم البحث

اقرأ أيضاً

81 - Yuri G. Zarhin 2020
We deal with $g$-dimensional abelian varieties $X$ over finite fields. We prove that there is an universal constant (positive integer) $N=N(g)$ that depends only on $g$ that enjoys the following properties. If a certain self-product of $X$ carries an exotic Tate class then the self-product $X^{2N}$of $X$ also carries an exotic Tate class. This gives a positive answer to a question of Kiran Kedlaya.
269 - Yuri G. Zarhin 2020
These are notes of my lectures at the summer school Higher-dimensional geometry over finite fields in Goettingen, June--July 2007. We present a proof of Tates theorem on homomorphisms of abelian varieties over finite fields (including the $ell=p$ c ase) that is based on a quaternion trick. In fact, a a slightly stronger version of those theorems with finite coefficients is proven.
81 - Yuri G. Zarhin 2020
Let $X$ be a polarized abelian variety over a field $K$. Let $O$ be a ring with an involution that acts on $X$ and this action is compatible with the polarization. We prove that the natural action of $O$ on $(X times X^t)^4$ is compatible with a certain principal polarization.
65 - Yuri G. Zarhin 2020
We study endomorphisms of abelian varieties and their action on the l-adic Tate modules. We prove that for every endomorphism one may choose a basis of each Tate module such that the corresponding matrix has rational entries and does not depend on l.
120 - Adrian Vasiu 2003
We extend to large contexts pertaining to Shimura varieties of Hodge type a result of Zink on the existence of lifts to characteristic 0 of suitable representatives of certain isogeny classes of abelian varieties endowed with Frobenius and other endo morphisms over $dbF_{p^q}$, whose $p$-divisible groups in mixed characteristic $(0,p)$ are with complex multiplication.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا