bio | website | |
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visits | member for | 1 year, 2 months |
seen | Sep 14 at 12:51 | |
stats | profile views | 254 |
Will no longer participate --- there are simply too many ill-behaved questioners.
Jul 3 |
awarded | Yearling |
Mar 6 |
awarded | Enlightened |
Mar 6 |
awarded | Nice Answer |
Feb 7 |
comment |
semisimple category with finite number of simple objects
See the answer: mathoverflow.net/questions/155617/ |
Feb 3 |
comment |
Steenrod operations in algebraic geometry
Atiyah and Hirzebruch used Steenrod operations to show that not all torsion cohomology classes are algebraic (this was originally considered to be part of the Hodge conjecture). The point is that certain Steenrod operations must vanish on torsion algebraic classes, but they don't vanish on all torsion classes. |
Jan 31 |
comment |
Zariski density of Q-bar points
Choose a basis $(e_i)$ for $\mathbb{C}$ over $\bar{\mathbb{Q}}$, and write $f=\sum e_i f_i$ where the $f_i$ are polynomials with coefficients in $\bar{\mathbb{Q}}$. Because $f$ vanishes on the $\bar{\mathbb{Q}}$-points of $X$, so does each $f_i$, and so lies in the (radical of) the ideal defining $X$ over $\bar{\mathbb{Q}}$. Hence vanishes on the $\mathbb{C}$ points. |
Jan 30 |
comment |
Uniqueness of composition series for profinite groups
Did you check whether the proof of the (Zassenhaus) Butterfly Lemma applies in your situation? It doesn't use much --- only the Noether isomorphism theorems and one of Dedekind's modular laws. That would imply that any two such sequences have a common refinement. |
Jan 29 |
comment |
Shimura varieties of type C
Yes --- PEL Shimura varieties are uncommon among those of Hodge type. Is the Shimura variety attached to $PGL_2$ of PEL-type? |
Jan 27 |
comment |
is the Hodge conjecture birationally invariant?
In fact, the Hodge conjecture, the Tate conjecture, and the various standard conjectures hold for all varieties if they hold for all rational varieties (and they do all hold for $\mathbb{P}^n$). See: Tankeev, S. G. Monoidal transformations and conjectures on algebraic cycles. (Russian) Izv. Ross. Akad. Nauk Ser. Mat. 71 (2007), no. 3, 197--224; translation in Izv. Math. 71 (2007), no. 3, 629--655 |
Jan 25 |
answered | how to see CM types as functions on the Galois group? |
Jan 24 |
answered | number of simple representations |
Jan 24 |
comment |
number of simple representations
The number is finite only for finite groups (at least among split groups). |
Jan 23 |
awarded | Nice Answer |
Jan 23 |
comment |
$S$-Tate-Shafarevich groups of elliptic curves
The problem is only for torsion at primes in S. More precisely, let m be an integer not divisible by any prime in S. Then the subgroup of the S Tate-Shafarevich group killed by some power of m coincides with the similar subgroup of the usual Tate-Shafarevich group. This is a standard result (see for example Milne's Arithmetic Duality Theorems I, 6.6., but note that his S is the complement of yours). |
Jan 23 |
answered | Why aren't fields called “bodies” instead? |
Jan 21 |
comment |
Why people usually consider reductive groups in GIT?
Someone should mention that Mumford was mainly interested in constructing moduli schemes for curves and polarized abelian varieties, for which reductive groups suffice. |
Jan 19 |
comment |
History and motivation for Tannaka, Krein, Grothendieck, Deligne et al. works on Tannaka-Krein theory?
@quid I disagree with you. Récoltes et Semailles contains a large number of very unpleasant statements about mathematicians, many totally false. Repeating them here serves no useful purpose. |
Jan 19 |
comment |
History and motivation for Tannaka, Krein, Grothendieck, Deligne et al. works on Tannaka-Krein theory?
Some corrections: the error in Saavedra's thesis is where he "proves" that fibre functors are locally isomorphic (not the existence). In fact, with his definition of Tannakian category they aren't (so the fibre functors don't form a gerbe). For this it is necessary to require that End(1)=k. The error was discovered by Deligne, pointed out in Deligne and Milne, and corrected later (with some difficulty) by Deligne. |
Jan 19 |
comment |
History and motivation for Tannaka, Krein, Grothendieck, Deligne et al. works on Tannaka-Krein theory?
@Olivier: Why do you keep repeating Grothendieck's paranoid rantings? The suggestion that Deligne intentionally ignored Saavedra's error so that he could get the glory himself is libelous nonsense. If you want to know the true story of Saavedra's thesis, I suggest that you ignore Grothendieck and talk to Deligne. |
Jan 19 |
comment |
History and motivation for Tannaka, Krein, Grothendieck, Deligne et al. works on Tannaka-Krein theory?
What Grothendieck says about Saavedra's thesis in Récoltes et Semailles is so unreliable, I wouldn't dignify it as giving "one side of the story". Deligne, who was effectively Saavedra's adviser for his last two years, has a very different view. I'm prepared to believe that Saavedra proved less than Grothendieck hoped was true, but because the (Grothedieck's?) definition of a Tannakian category was wrong, what Grothendieck hoped probably wasn't actually true. |