bio | website | mathematik.uni-mainz.de/… |
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location | Mainz | |
age | 27 | |
visits | member for | 5 years, 1 month |
seen | 16 hours ago | |
stats | profile views | 2,766 |
Post-doc at Johannes-Gutenberg Universität Mainz. Interested in many things, but especially arithmetic geometry.
Apr 22 |
revised |
Separation condition for higher Deligne-Mumford stacks
deleted 3 characters in body |
Apr 22 |
revised |
Finiteness of the connected components of a stack
edited title |
Mar 29 |
comment |
When does an algebraic space that is a torsor over a scheme have to be a scheme?
Check out arxiv.org/abs/1501.04304 . |
Mar 24 |
revised |
Abelian varieties with good reduction everywhere over function fields
edited tags |
Mar 24 |
answered | Abelian varieties with good reduction everywhere over function fields |
Mar 22 |
comment |
$\mathcal{M}_{g,n}$ a scheme for $n \gg 0$?
@TimoKeller To answer your question in the comments of the other question, see Corollary 8.1.1 in the book Champs Algebriques by Laumon and Moret-Bailly: Any DM stack with trivial stabilizers is an alg space. To see that an alg space is a scheme you can apply Knudson's criterion sometimes and use properties of the coarse moduli space as S. Carnahan mentions. (For Knudson's criterion see Cor. II.6.16 of his book on Alg Spaces.) |
Mar 2 |
awarded | Yearling |
Feb 18 |
comment |
Automorphisms of generic complete intersections
...the problem therefore becomes showing the analogue of 2). Namely, showing the injectivity of the canonical map $Aut(X) \to Aut(H^n_{prim}(X)$ (which is easy in fact if $\sum d_i > n+1$). As you note, 1) and 2) only show that the generic autom group is then trivial or $\mathbb Z/2\mathbb Z$. To exclude that there are autom's acting as $-1$ on cohomology (ie. prove 3) might be a bit difficult because as you say the (highly singular) quotient will be a fake projective space. The only way to do this I know of is using Lefschetz trace formula. |
Feb 18 |
comment |
Automorphisms of generic complete intersections
The argument you have in mind (I think) also appears in the book of Katz-Sarnak when they show that the generic autom group of a smooth curve of genus $g>1$ is trivial. They do this by combining 1) the bigness of the monodromy group with 2) the injectivity of the map $Aut(X) \to Aut(H^1(X))$ and 3) the fact that a generic curve $X$ is not hyperelliptic (so that no automorphism of $X$ induces $-1$ on $H^1$). In the case of complete intersections, the bigness still holds (see the book by Peters-Steenbrink for a reference).... |
Feb 17 |
revised |
Mumford-Tate groups of products of Hodge structures
Fixed a small typo |
Feb 2 |
revised |
What implications would a solution of the *Standard Conjectures* have on the *Hodge Conjecture*?
added 1 character in body |
Jan 19 |
answered | there exists a hypersurface H ⊂ X such that X \ H is Stein and L is trivial over X \ H |
Jan 15 |
reviewed | Approve The Metrizability of Symmetric Products of Metric Spaces |
Jan 14 |
revised |
Isotriviality: two definitions
deleted 1 character in body |
Jan 14 |
answered | Isotriviality: two definitions |
Dec 29 |
comment |
sanity check about a morphism from a stack to its coarse moduli space
@TomGraber Thank you for your comment. I think User74230 meant to write "quasi-finite" instead of "etale". This makes me wonder: aren't all etale morphisms representable? |
Dec 25 |
answered | sanity check about a morphism from a stack to its coarse moduli space |
Dec 21 |
comment |
An extension of group schemes admitting Neron models
On the other hand, the implications a implies b and a implies e of Thm 10.2.1 hold in general (as you probably already know). There might be a way to circumvent the compactification results and to prove that a group scheme not containing any copy of G_a or G_m is "bounded" directly (but I doubt it...). |
Dec 21 |
comment |
An extension of group schemes admitting Neron models
If I'm not mistaken, the necessary "compactification" resuts used in Thm 10.2.1 are now known for not necessarily commutative group schemes by the work of Gabber. Try googling Gabber's compactification theorem to see if you get something useful. |
Dec 21 |
reviewed | Reject Refereeing a Paper |