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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. |
Nov
28 |
comment |
Fermat's last theorem over larger fields
See also Zarhin-Parshin, "Finiteness theorems...", p. 92 for a related conjecture (also made by Mazur). |
Nov
26 |
comment |
How to see that this pairing of line bundles is multiplicative?
Do you want a canonical isomorphism (inv. under base-change) ? Or would you be happy with any isomorphism ? |
Nov
19 |
accepted | On a proposition in Hartshorne's paper “Ample vector bundles on curves” |
Nov
16 |
awarded | Nice Question |
Nov
16 |
comment |
On a proposition in Hartshorne's paper “Ample vector bundles on curves”
Thank you very much for taking the time to write this answer. If I understand your answer right, your construction is in the same line as what ulrich described in his comment. I would still like to see a proof or a counterexample to Prop. 4.1, though but if nobody provides one in the next few days I will accept your answer. |
Nov
15 |
comment |
On a proposition in Hartshorne's paper “Ample vector bundles on curves”
@ulrich. Thank you very much for this interesting comment. That settles it then, as far as (X) is concerned. Here is a possible simplification of your argument: as you write, $C\to f(C)$ must be generically separable because $H^0(A,\Omega_A)\to H^0(C,\Omega_C)$ does not vanish. Now since $C\to f_*(C)$ is also generically inseparable, it must be birational. Note that $f_*(C)$ might be singular, so its geometric genus might not be defined (or is there a way to show that it must be non-singular ?). |