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32 votes

How does one see Hecke Operators as helping to generalize Quadratic Reciprocity?

number-theory intuition modular-forms quadratic-reciprocity asked Aug 7 '11 at 0:20
math.stackexchange.com

20 votes

In what sense is Taniyama-Shimura the $n=2$ case of Langlands?

number-theory modular-forms asked Aug 3 '11 at 23:22
math.stackexchange.com

13 votes

Different formulations of Class Field Theory

algebraic-number-theory asked Dec 20 '10 at 2:12
math.stackexchange.com

13 votes

Is $\bar{\mathbb{Q}}(x)\cap \mathbb{Q}((x))=\mathbb{Q}(x)$? [unsolved (even though we earlier thought it was)]

abstract-algebra number-theory field-theory asked Feb 12 '12 at 0:04
math.stackexchange.com

11 votes

Why is $O_K\otimes \mathbb{Z}_p\cong \oplus_{\mathfrak{p}|p}O_{K,\mathfrak{p}}$?

abstract-algebra number-theory commutative-algebra p-adic-number-theory asked Apr 28 '12 at 2:43
math.stackexchange.com

10 votes

What is the intuition behind the concept of Tate twists?

number-theory algebraic-geometry intuition asked Aug 16 '11 at 4:06
math.stackexchange.com

9 votes

Interpretations of the first cohomology group

group-theory group-cohomology asked Dec 27 '11 at 17:48
math.stackexchange.com

8 votes

Is $\operatorname{Gal}(\mathbb{Q}_p^{un})\cong \hat{\mathbb{Z}}$?

number-theory algebraic-geometry field-theory galois-theory asked Feb 23 '12 at 5:45
math.stackexchange.com

8 votes

Is spacetime simply connected?

general-relativity spacetime universe differential-geometry topology asked Jul 8 '11 at 1:26
physics.stackexchange.com

8 votes

Could cell-phone radiation cause cancer?

electromagnetic-radiation asked Jul 8 '11 at 22:24
physics.stackexchange.com

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