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Yes. For elementary reasons. Suppose it weren't dense. Then there would be some little interval not hit, of some positive length say $1/N$. But this cannot happen. Divide the circle into N little eq …

I have spent some time being confused by the nature of global methods in number theory. It seems that there are in some sense (for my purposes) three levels at which algebraic number theorists operate …

Without the restriction on the lie algebra, certainly. There are interesting examples of families of abelian varieties with (generically) no extra endomorphisms but whose generic Mumford-Tate group is …

My question refers to the paper http://arxiv.org/pdf/alg-geom/9710020.pdf where Batyrev proves that birational Calabi-Yau algebraic varieties have equal Betti numbers by counting points over finite fi …

I am a total non-expert, so the answer to this question may be obvious, but here goes. In Chevalley's formulation of CFT we get Artin maps $J_k \rightarrow Gal(L/k)$, where $J_k$ is the group of all …

In the theory of automorphic representations one says that G satisfies a "multiplicity one" property if every cuspidal representation occurs with multiplicity one in $L^2(G(F)\backslash G(A))$. One a …

Perhaps this is a bit too 'standard' for MO, but I'm struggling to dig it out of the literature (and maybe other people have had a similar experience), so it feels like a useful thing to ask and I hop …

The following is (very) well known. Let's assume $f$ is a normalised newform of weight $k \geq 2$, nebentype $\chi$ with $p$th Fourier coefficient $a_p$. Then your representation $\rho_{f,p}$ (obtaine …

Suppose I have a smooth non-proper algebraic variety $X/\mathbb{C}$. A vector bundle with flat connection (``differential equation'') on $X$ extends, as was noted by Grothendieck, to a coherent crys …

Fix a scheme $S$, a group scheme $G/S$ (let us say smooth, maybe even affine with some finiteness conditions if you like), and suppose I have some other $S$-scheme $P$ with a right $G$-action. We want …