bio  website  math.uga.edu/~pete 

location  Athens, GA  
age  39  
visits  member for  5 years, 10 months 
seen  1 hour ago  
stats  profile views  29,011 
assistant associate prof of math @ University of Georgia.
Primary research interests: number theory, arithmetic geometry, Galois cohomology
Secondary research interests: field theory, commutative algebra, general topology, model theory, and various combinations thereof
I also have an enduring interest in mathematical exposition.
NOTE: In Spring 2015 my department adjusted the mechanics of its webpage, which broke a lot of my links. For now, if you see a broken link like http://www.math.uga.edu/~pete/inversemw.pdf, try changing it to http://math.uga.edu/~pete/inversemw.pdf. It should fix the problem.
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awarded  Stellar Question 
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awarded  Popular Question 
Aug
30 
revised 
Integrability of derivatives
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28 
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21 
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Aug
14 
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Is Monsky's theorem depending on axiom of choice ?
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2 
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Jul
7 
comment 
uncountable algebraically closed field other than C ?
@potentially dense: See $\S$12.2 of math.uga.edu/~pete/FieldTheory.pdf. Alternately, as the comments describe, from a model theoretic perspective this is a consequence of the model completeness of the theory of algebraically closed fields, itself a corollary of quantifier elimination in such fields. For that perspective, see $\S$5.4 of math.uga.edu/~pete/modeltheory2010FULL.pdf. (Or better, see any introductory model theory text whatsoever...) 
Jul
7 
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A quasicompact space with a net that contains no convergent strict subnet
In other words...compact does not imply sequentially compact. 
Jun
19 
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1 
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Is there an introduction to probability theory from a structuralist/categorical perspective?
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May
30 
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Naturally occuring groups with cardinality greater than the reals.
@few__reps: Certainly; this kind of cardinality construction is pursued in more generality in math.uga.edu/~pete/settheorypart4.pdf. The point is that it trivially works for all infinite cardinals, so it is precisely what I mean to exclude when I asked (not so precisely) for a "natural example". 
May
30 
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May
27 
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What are the most misleading alternate definitions in taught mathematics?
@Alexey: Yes, you are using that $a \mapsto \overline{a}$ is a group homomorphism and that addition in $\mathbb{Z}$ is associative. 
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