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7132280
bio website math.uga.edu/~pete
location Athens, GA
age 38
visits member for 5 years, 1 month
seen 2 days ago
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.

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comment Is there a proof of Warning's Second Theorem using p-adic cohomology?
Thanks, ACL. When I get the chance, perhaps I'll contact you and ask/say a bit more.
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revised Is there a proof of Warning's Second Theorem using p-adic cohomology?
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comment Is there a proof of Warning's Second Theorem using p-adic cohomology?
My feeling on this is as follows: Warning's Second Theorem is an "Archimedean" inequality, not a $p$-adic congruence. It is known that it does not follow from the strongest possible $p$-adic congruence (Ax-Katz). Thus I find it counterintuitive that it could come out this way. So if you could show me such a proof even in the smooth homogeneous case, I would be quite interested.
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revised Is there a proof of Warning's Second Theorem using p-adic cohomology?
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asked Is there a proof of Warning's Second Theorem using p-adic cohomology?
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comment If all balls at $x$ and $y$ are isometric is there an isometry sending $x$ to $y$?
For my part, I found this answer to be elegant and easy to understand. While thinking about it, I got a "model-theoretic flash": it reminds me of issues of "local isomorphism" which arise in that subject. I wonder if one can make a real connection there...
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comment Minimal model of a non-singular complex projective surface defined over $\overline{\mathbb Q}$
Hartshorne, Theorem V.5.7, proves Castelnuovo's Criterion over any algebraically closed field.
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revised Minimal model of a non-singular complex projective surface defined over $\overline{\mathbb Q}$
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answered Minimal model of a non-singular complex projective surface defined over $\overline{\mathbb Q}$
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