bio | website | math.utah.edu/~schwede |
---|---|---|
location | Utah | |
age | 36 | |
visits | member for | 5 years, 7 months |
seen | 9 hours ago | |
stats | profile views | 5,652 |
I'm an associate professor at the University of Utah. I work on algebraic geometry and commutative algebra.
Aug
24 |
comment |
Serre duality over a non-algebraically closed field
True. I guess it depends on exactly what statement you are looking for. |
Aug
24 |
answered | Serre duality over a non-algebraically closed field |
Aug
23 |
reviewed | Close A chinese remaindering problem |
Aug
23 |
comment |
Serre duality over a non-algebraically closed field
See Grothendieck duality, then you get statements over much more general bases. |
Aug
18 |
reviewed | Leave Open Training towards research on k3 surfaces |
Aug
17 |
reviewed | Leave Open Mathematical software wish list |
Aug
17 |
reviewed | Close addition on an affine scheme |
Aug
16 |
comment |
addition on an affine scheme
Yes, it is not defined on affine schemes in general certainly. |
Aug
15 |
comment |
addition on an affine scheme
Can you be more specific as to where this statement is? Maybe provide a link? |
Aug
15 |
comment |
Vanishing for ideal sheaves on spaces with only rational singularities
Maybe it's worth pointing out that for isolated singularities, one has the injection $R^{i} \pi_* \mathcal{O}_Y(-E) \hookrightarrow R^{i} \pi_* \mathcal{O}_Y$, then the vanishing you want holds very easily. See for instance Mixed Hodge structures associated with isolated singularities by Steenbrink for a topological argument. One can also deduce this by the degeneration of the Hodge-to-De Rham spectral sequence. |
Aug
15 |
reviewed | Close Jacobson radical of an indecomposable commutative ring |
Aug
10 |
comment |
Do we know when $R^if_*\omega_{Y}$ is k-th syzygy sheaf?
See for instance section 7 of arxiv.org/pdf/0902.0648.pdf I guess they are assuming also twisting $\omega_Y$ by high powers of relatively ample line bundles, so that probably is non-optimal for you... The case where that's not needed is if you have a family of Calabi-Yaus (see the above reference). |
Aug
10 |
reviewed | Close The trace ideal of a non zero $R$-module |
Aug
10 |
comment |
Do we know when $R^if_*\omega_{Y}$ is k-th syzygy sheaf?
There are cases when you know such higher direct images are locally free when $f$ is flat and the fibers have nice singularities, is that good enough for you? Sorry, I don't remember the definition of a $k$th syzygy sheaf (Maybe you can provide a link to the actual definition?) |
Jul
23 |
reviewed | Leave Open Why should we regard $PL(M)$ as a simplicial group? |
Jul
23 |
reviewed | Leave Open The scheme $y^n = x^{2n}$ for $n$ a rational number |
Jul
22 |
comment |
pull back of an ample line bundle under a blow up
Is $Y$ itself also smooth (then the answer is yes, see for instance Hartshorne's section on blowups)? If not, are you defining $E$ to the subscheme defined by $I_Z \cdot O_X$? Or are you defining it to the the divisorial part of the exceptional set (with what scheme structure)? Depending on your answer, the answer is also yes... |
Jul
4 |
reviewed | Leave Open Stability of the Solar System |
Jun
23 |
reviewed | Leave Open How do I evaluate this sum :$\sum_{n=0}^{\infty} \frac{\sin(n!)}{\cos(n!)}$ if it's not open problem? |
Jun
23 |
reviewed | Leave Open Is $\sqrt {2 \sqrt {3 \sqrt {4 \ldots}}}$ a rational number? |