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Oct
18 |
comment |
Are there any good computer programs for drawing (algebraic) curves?
If you have access to Mathematica and it produces the diagram you want, fine, but for more control use gnuplot+tikz. |
Oct
17 |
comment |
Awfully sophisticated proof for simple facts
Brauer groups and cohomology are certainly overkill for Wedderburn's theorem: if $D$ is a finite division algebra and $L$ is a maximal subfield, then the Noether-Skolem theorem shows that the multiplicative group of $D$ is a union of conjugates of that of $L$; hence $D$=$L$. |
Oct
14 |
comment |
Chapters 1--4 of the Artin-Tate notes on Class Field Theory
As far as I know, the notes for the first part of the seminar were never written up. Lang missed this part of the seminar because he started as a philosophy student. |
Oct
7 |
comment |
who fixed the topology on ideles?
Yes, I think the answer is Weil. In his short 1936 paper "Remarques sur des resultats recent de C. Chevalley" he complains about Chevalley's topology, and writes down other constructions and topologies (and mentions Grossencharacters) but doesn't write down anything immediately recognizable (to me) as the ideles. In his 1951 paper (J. Math. Soc. Japan) he defines without comment the ideles with the natural (modern) topology. That is also where he wrote "La recherche d'une interpretation pour C_k ... me semble constituer l'un des problemes fondamentaux..." See also his Commentaries in his CW. |
Oct
3 |
comment |
Is a torsion free abelian group finitely generated, if all of its localizations at primes p are finitely generated over Zp?
Have you seen the erratum jmilne.org/math/CourseNotes/errata.html#AV ? |
Sep
24 |
answered | Math keyboard: does it exist ? |
Sep
21 |
comment |
Are there motives which do not, or should not, show up in the cohomology of any Shimura variety?
Blasius has pointed out that the naive generalization of the modularity conjecture fails --- there exist elliptic curves over number fields that are not quotients of the albanese of any Shimura variety --- but I don't know of any reason why the more general version (4) can't be true. (Blasius 2004 MR2058605). |
Sep
11 |
comment |
What heuristic evidence is there concerning the unboundedness or boundedness of Mordell-Weil ranks of elliptic curves over $\Bbb Q$?
Cassels said it best (JLMS 1966, p.257):... it has been widely conjectured [on the basis of calculations] that there is an upper bound for the rank depending only on the groundfield. This seems to me implausible because the theory makes it clear that an abelian variety can only have high rank if it is defined by equations with very large coefficients. . (For there must be a lot of alternative factorizations to be possible in the arguments of §24.) |
Sep
10 |
revised |
Is the category of commutative group schemes abelian?
added 1041 characters in body |