13,362 reputation
22456
bio website math.utah.edu/~schwede
location Utah
age 35
visits member for 4 years, 11 months
seen 6 hours ago

I'm an associate professor at the University of Utah. I work on algebraic geometry and commutative algebra.


6h
reviewed Close Looking for comparison of the “cost” of computation of two algorithms
14h
reviewed Leave Open Why is $ \frac{\pi^2}{12}=\ln(2)$ not true?
Dec
22
comment Extension of homomorphism to place in quotient field, or of local ring to valuation ring in quotient field
You mean infinite? This is not too hard, geometrically blow up the origin, then there are infinitely many points on that $\mathbb{P}^1$. If you blowup any one of those points, that gives a distinct discrete valuation lying over the origin. The residue field of every such valuation ring is a transcendental (degree = 1) extension of $\mathbb{Q}$.
Dec
22
comment How would you call a variety that is locally a complete intersection up to defect c?
I haven't seen a name for it either.
Dec
22
awarded  ac.commutative-algebra
Dec
21
comment Connected curve
Hi Jason, the first example I wrote was with $D$ empty (if you look at the revision history), but then I thought that the op would probably want something with $D$ non-empty and with non-empty transverse intersection with $C$.
Dec
21
answered Connected curve
Dec
21
comment Connected curve
Do you mean $X \setminus D$? Also, what makes a divisor simple? Are you assuming that $W$ is connected (otherwise there is no hope)? Even so, assuming I'm reading this right, it seems very unlikely to be true. Do you have any reason to believe it's true? Have you tried any examples?
Dec
21
comment Extension of homomorphism to place in quotient field, or of local ring to valuation ring in quotient field
What are you expecting? There can and usually are infinitely many such extensions, right? (Think about all the valuation subrings of $Q(x,y)$, discrete or otherwise, lying over the origin of $Q[x,y]$. Or did I misunderstand what you were asking?). Also, what is $\tilde \varphi$ in your question.
Dec
21
reviewed Leave Open What's so special about $1$-categories?
Dec
21
reviewed No Action Needed on the existence of holomorphic coordinates under bounded curvature
Dec
20
reviewed Leave Closed Connected components $0-1$ matrices
Dec
19
reviewed Close Cylinder in a topological space?
Dec
18
comment intuitive interpretation of analytic spread
I don't think I can do that here, but I would suggest you read a little algebraic geometry (for instance, the first and second chapter of Hartshorne would cover all of this).
Dec
17
revised intuitive interpretation of analytic spread
added 141 characters in body
Dec
17
answered intuitive interpretation of analytic spread
Dec
17
reviewed Leave Open intuitive interpretation of analytic spread
Dec
16
reviewed Leave Open How prove this polynomial inequality from a book
Dec
15
comment what are the possible approximations for ideals
Reflexification will generally be bigger. I don't think you can see it via projecting to DVRs (unless you want an infinite collection of DVRs, those corresponding to height one primes of your ring). Can you say more about your particular collection of ideals.
Dec
15
comment what are the possible approximations for ideals
Reflexification isn't so bad. It's just applying the functor $Hom_R(\bullet, R)$ to the ideal, twice. This can be quite quick in a computer (or at least, usually it isn't the thing that usually kills you in a computer).