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Results tagged with arithmetic-geometry
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user 5513
Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
12
votes
Can one ignore primes lying over $l$ in the Fontaine-Mazur conjecture? Counterexamples?
In fact there are one-dimensional counterexamples: if $\chi$ is the $l$-adic cyclotomic character, and $k\in \mathbb{Z}_l \backslash \mathbb{Z}$, then $\chi^{(l-1)k}$ is unramified outside $l$, but do …
- 4,790
3
votes
The significance of modularity for all Galois representations
Proving modularity of finite image Galois representations seems to be the most feasible way of proving the Artin conjecture. In fact, this was one of Langlands' original motivations.
- 4,790