Global Galois Symbols on E x E

2024/07/29 by Ramakrishnan, Dinakar
#11G07 #11G10 #14C25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2407.20468

Abstract

Let E be an elliptic curve over a number field F, A the abelian surface E x E, and T_F(A) the F-rational albanese kernel of A, which is a subgroup of the degree zero part of Chow group of zero cycles on A modulo rational equivalence. The first result is that for all but a finite number of primes p where E has ordinary reduction, the image of T_F(A)/p in the Galois cohomology group H²(F, sym²(E[p])) is zero; here E[p] denotes as usual the Galois module of p-division points on E. The second result is that for any prime p where E has good ordinary reduction, there is a finite extension K of F, depending on p and E, such that T_K(A)/p is non-zero. Much of this work was joint with Jacob Murre, and the article is dedicated to his memory.

Related

• Local Galois Symbols on E x E
• Zero cycles on products of elliptic curves over local fields with supersingular reduction
• On uniform lower bound of the Galois images associated to elliptic curves
• Zero-cycles on a product of elliptic curves over a p-adic field
• On the cycle map for products of elliptic curves over a p-adic field