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On the Invariant of Chen-Kuan for Abelian Varieties

문현숙
경북대학교 자연과학대학 수학과|2016.09|Kyungpook Mathematical Journal|제56권 제3호|pp. 755-761

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참고문헌

키워드

torsion pointsGalois representationsGalois orbits.
주제분류수학

초록

Let $A$ be an abelian variety over a global field $K$. We show that, in ``many'' cases,Chen-Kuan's invariant $M(A[n])$,that is the average number of $n$-torsion pointsof $A$ over various residue fields of $K$, hasthe minimal possible value.

Abstract

Let $A$ be an abelian variety over a global field $K$. We show that, in ``many'' cases,Chen-Kuan's invariant $M(A[n])$,that is the average number of $n$-torsion pointsof $A$ over various residue fields of $K$, hasthe minimal possible value.

참고문헌 (5)

  1. Yen-Mei J. Chen, "On the distribution of torsion points modulo primes", Bull. Aust. Math. Soc., 86, pp.339~347 (2012)
  2. P. M. Cohn, "Algebra" (1991), John Wiley & Sons
  3. Hsiu-Lien Huang, "The average number of torsion points on elliptic curves", J. Number Theory, 135, pp.374~389 (2014)
  4. H. Moon, "On the invariant M(A=K; n) of Chen-Kuan for Galois representations", Proc. Japan Acad., 90, pp.98~100 (2014)
  5. J.-P. Serre, "Resume des cours de 1985-1986", Annuaire du College de France, pp.95~99 (1986)

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