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Jul
3 |
awarded | Yearling |
Jul
3 |
comment |
Idea of using etale site
@wkf Reference? Did you check the reference in my comment yesterday? |
Jul
3 |
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 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. |