bio  website  math.utah.edu/~schwede 

location  Utah  
age  35  
visits  member for  4 years, 11 months 
seen  6 hours ago  
stats  profile views  5,056 
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.commutativealgebra 
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 $D$ nonempty and with nonempty 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 $01$ 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). 