Global Galois Symbols on E x E
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917841473634304 |
|---|---|
| author | Ramakrishnan, Dinakar |
| author_facet | Ramakrishnan, Dinakar |
| contents | 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 H^2(F, sym^2(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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20468 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global Galois Symbols on E x E Ramakrishnan, Dinakar Number Theory Algebraic Geometry 11G07, 14C25, 11G10 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 H^2(F, sym^2(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. |
| title | Global Galois Symbols on E x E |
| topic | Number Theory Algebraic Geometry 11G07, 14C25, 11G10 |
| url | https://arxiv.org/abs/2407.20468 |