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bio website jmilne.org/math
location Ann Arbor, MI, USA, and New Zealand.
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visits member for 5 years, 2 months
seen Oct 18 '10 at 13:35
Arithmetic geometry (especially Shimura varieties and abelian varieties).

Jul
7
awarded  Nice Answer
Apr
29
awarded  Nice Answer
Nov
10
awarded  Pundit
Oct
30
awarded  Nice Answer
Oct
28
awarded  Good Answer
Oct
22
awarded  Yearling
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
comment Is the category of commutative group schemes abelian?
Thanks - fixed.
Sep
10
revised Is the category of commutative group schemes abelian?
added 1041 characters in body
Sep
10
awarded  Nice Answer
Sep
9
answered Is the category of commutative group schemes abelian?
Sep
1
comment Is there a classification of embeddings of SL_2 into SP_6 as algebraic groups over Q and R respectively?
Assume the base field has characteristic zero. The category of representations of a semisimple Lie algebra is Tannakian, and the algebraic group attached to this category is the simply connected algebraic group with the given Lie algebra. A homomorphism of Lie algebras defines a tensor functor of the Tannakian categories, and hence a homomorphism of the corresponding simply connected algebraic groups.
Aug
31
comment Why aren't there more classifying spaces in number theory?
Continued: It was then found that $H^{1}$ coincided with the group of crossed homomorphisms modulo principal crossed homomorphisms, and $H^{2}$ with the group of equivalence classes of "factor sets", which had been introduced much earlier (e.g., I. Schur, \"{U}ber die Darstellung der endlichen$\ldots$ , 1904; O. Schreier, \"{U}ber die Erweiterungen von Gruppen, 1926; R. Brauer, \"{U}ber Zusammenh\"{a}nge$\ldots$ , 1926). For more on the history, see MacLane 1978 (Origins of the cohomology of groups. Enseign. Math. (2) 24 (1978), no. 1-2, 1--29. MR0497280).