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visits  member for  2 years 
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Will no longer participate  there are simply too many illbehaved questioners.
21h

awarded  Yearling 
1d

comment 
Idea of using etale site
@wkf Reference? Did you check the reference in my comment yesterday? 
1d

comment 
Idea of using etale site
For the origins of etale cohomology, see the article "The Riemann Hypothesis..." on Milne's website. 
Sep 24 
awarded  Autobiographer 
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 Qbar 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 PELtype? 
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, 197224; translation in Izv. Math. 71 (2007), no. 3, 629655 
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 
$S$TateShafarevich 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 TateShafarevich group killed by some power of m coincides with the similar subgroup of the usual TateShafarevich 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. 