3,257 reputation
1938
bio website mathematik.uni-mainz.de/…
location Mainz
age 27
visits member for 5 years, 3 months
seen 3 hours ago

Post-doc at Johannes-Gutenberg Universität 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