14,397 reputation
32561
bio website math.utah.edu/~schwede
location Utah
age 36
visits member for 5 years, 7 months
seen 9 hours ago

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?