bio | website | mathematik.uni-mainz.de/… |
---|---|---|
location | Mainz | |
age | 27 | |
visits | member for | 5 years, 3 months |
seen | 3 hours ago | |
stats | profile views | 2,811 |
Post-doc at Johannes-Gutenberg UniversitÃ¤t Mainz. Interested in many things, but especially arithmetic geometry.
May 27 |
answered | Obstruction to get a galois invariant cycle |
May 18 |
reviewed | Approve What is prime power of this equation of p? |
May 15 |
revised |
Abelian varieties with good reduction everywhere over function fields
Added a sentence to explain second paragraph of answer |
May 15 |
reviewed | Approve Kernel of flux homomorphism (Calabi invariant) for volume-preserving maps on a compact manifold |
May 12 |
reviewed | Approve Algebraic proof of Five-Color Theorem using chromatic polynomials by Birkhoff and Lewis in 1946 |
May 12 |
reviewed | Approve Question about divisors and its images |
May 6 |
comment |
Do line bundles descend to coarse moduli spaces of Artin stacks with finite inertia?
Dear @ZsoltPatakfalvi, you're right. That's not a good test case. |
May 5 |
comment |
Do line bundles descend to coarse moduli spaces of Artin stacks with finite inertia?
@ZsoltPatakfalvi Is this true for the stack of smooth curves of genus one $\mathcal M_1$? Note that $\mathcal M_1$ is a smooth separated finite type Artin (but not DM) stack over $\mathbb Z$. |
May 5 |
comment |
manifold branched covering space for orbifolds
In the algebraic setting every smooth orbifold is a global quotient stack; see Thm 2.18 in arxiv.org/pdf/math/9905049v3.pdf |
May 5 |
comment |
manifold branched covering space for orbifolds
I'm a bit confused. You write "Not every orbifold is a global quotient", but then later you write "every orbifold is a global quotient $M/G$. |
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 |