3,237 reputation
1938
bio website mathematik.uni-mainz.de/…
location Mainz
age 27
visits member for 5 years, 1 month
seen 3 hours ago

Post-doc at Johannes-Gutenberg Universität Mainz. Interested in many things, but especially arithmetic geometry.


3h
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
Dec
20
answered Is there a Riemann existence theorem for orbifolds?
Dec
19
revised Weil height of an Abelian Variety with everywhere (potentially) good reduction
deleted 1 character in body