Bibliographic Details
| Title: |
Constructing abelian varieties from rank 2 Galois representations. |
| Authors: |
Krishnamoorthy, Raju, Yang, Jinbang, Zuo, Kang |
| Superior Title: |
Compositio Mathematica; Mar2024, Vol. 160 Issue 4, p709-731, 23p |
| Subject Terms: |
ABELIAN varieties, ELLIPTIC curves, COMPACTIFICATION (Mathematics) |
| Abstract: |
Let $U$ be a smooth affine curve over a number field $K$ with a compactification $X$ and let ${\mathbb {L}}$ be a rank $2$ , geometrically irreducible lisse $\overline {{\mathbb {Q}}}_\ell$ -sheaf on $U$ with cyclotomic determinant that extends to an integral model, has Frobenius traces all in some fixed number field $E\subset \overline {\mathbb {Q}}_{\ell }$ , and has bad, infinite reduction at some closed point $x$ of $X\setminus U$. We show that ${\mathbb {L}}$ occurs as a summand of the cohomology of a family of abelian varieties over $U$. The argument follows the structure of the proof of a recent theorem of Snowden and Tsimerman, who show that when $E=\mathbb {Q}$ , then ${\mathbb {L}}$ is isomorphic to the cohomology of an elliptic curve $E_U\rightarrow U$. [ABSTRACT FROM AUTHOR] |
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| Database: |
Complementary Index |
