Impact
~38k
people reached
- 0 posts edited
- 0 helpful flags
- 189 votes cast
Apr
19 |
comment |
“Parameterising” extensions $0\to E\to W\to F\to 0$ by $\mathbb P(H^1(E\otimes F^*))$?
I think you might be interested in the first section of the article by Mireille Martin-Deschamps, "Propriétés de descente des variétés à fibré cotangent ample, Ann. Inst. Fourier (Grenoble) 34 (1984), no. 3, 39–64. |
Feb
28 |
comment |
Extension of ample vector bundles is ample
@Count Dracula. Sorry I commented too quickly. The fact that the extension of an ample bundle by another ample bundle is ample is not very difficult to prove (see Jason's reference) but it is a subtle fact that in char. 0, a non-trivial extension of an ample bundle by a trivial bundle is ample. This is also proven in Lazarsfeld's book (and it false in char. p>0). |
Feb
26 |
comment |
Elementary proof of Chevalley's Theorem on constructible sets
I would say that the basic input in (one of the) proofs is Noether's normalisation lemma. I don't think that you can make it more elementary than that. |
Feb
26 |
comment |
Extension of ample vector bundles is ample
@abx This is no true in positive characteristic. For the general theory, see the first part of Martin-Dechamps, Propriétés de descente des variétés à fibré cotangent ample." Annales de l'institut Fourier 34.3 (1984). |
Feb
13 |
comment |
Zariski-closed subgroups of ${\mathbf G}_{\mathbf a}^n$
What about $\alpha_p:={\rm Spec}K[X]/X^p$? |
Jan
10 |
comment |
Which sheaves satisfy cohomological purity?
About this, see middle of p. 124 of the book by Kiehl-Weissauer on Weil Conjectures, Perverse sheaves etc. |
Sep
13 |
awarded | Necromancer |
Aug
22 |
awarded | Yearling |
Aug
3 |
comment |
Is this kind of scheme integral?
For smthg related to your question, see Prop 4.3.8 p. 137 in Liu book (this shows eg that if you assume that $X$ is flat over $R$ and $X_\eta$ is integral, then so is $X$). |
Jun
25 |
accepted | CM abelian varieties over the rationals |
Jun
25 |
comment |
CM abelian varieties over the rationals
Nice answer... thank you for that. I wonder why this argument does not appear in any of the usual references for the theory of complex multiplication (unless I missed something ?). |
Jun
24 |
asked | CM abelian varieties over the rationals |
Jun
17 |
comment |
Projective bundle formula
(you means $X={\bf P}(E)$ in your formula) If $X$ is smooth and proper, then by Hodge decomposition the formula is the same as for singular cohomology (see Griffiths-Harris, p. 606). If $X$ is smooth but not necessarily proper then the cohomology ring might be infinite-dimensional. |
May
16 |
comment |
Reference request: Cohomology of Elliptic Curves
Why is the image of $\mu_\nu$ a normal subgroup of ${\rm Gal}(K^{\rm ab}|K)$ ? Sorry if I missed something obvious. |
Apr
2 |
comment |
Connected vs Irreducible Subvarieties
What about normality ? |
Feb
25 |
comment |
A proper smooth surface is projective
Several classical references are given on II, §4, p. 105 of Hartshorne's book. |
Jan
25 |
comment |
References for general Hasse-Weil zeta function
I do not know any other coherent reference than "facteurs locaux".... |
Jan
5 |
comment |
automorphisms of local rings vs local change of coordinates
I think you haven't actually stated which two objects you want to coincide. |
Dec
14 |
comment |
Quotient of a (non-linear) algebraic group by a closed subgroup
Here is another reference: Raynaud, 'Passage au quotient par une relation d'équivalence plate', Proceedings of a conference on local fields (Driebergen, 1967), p. 82 Ex. a) (i). |
Nov
29 |
comment |
Fermat's last theorem over larger fields
Sorry, your are right, Mazur's conjecture does not quite cover your question (but it gives a partial answer). The conjecture in Zarhin-Parshin corresponds precisely to what follows from Mordell-Lang + Mazur's conjecture. |