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Results tagged with ag.algebraic-geometry
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user 37644
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
9
votes
Unexpected applications of transcendental number theory?
Tools from transcendence theory have been crucial to the most significant recent advances in problems of unlikely intersections. The strategy was first dreamed up by Zannier, I believe, and has been …
- 1,499
4
votes
0
answers
126
views
Bounding the dimension of the locus where a variety has larger than expected dimension
Disclaimer: I am a research mathematician, but not an algebraic geometer, and so I don't know if this is a good question. I welcome advice for improving it and/or better tags.
Let $K$ be an infini …
- 1,499
4
votes
How much do I need to learn algebraic geometry to understand arithmetics over number fields
I'm going to say no: it's not necessary to know the modern algebraic geometry to explore the theory of rational points of algebraic varieties. Obviously, as pointed out in some of the answers, it's h …
- 1,499
2
votes
0
answers
323
views
PAC field : Algebraically closed field :: ? : Henselian local ring
I'm wondering if the following exists in the world as a definition. I'll use the word "pseudo-Henselian." I'll restrict to DVRs for simplicity.
I'd want to call a DVR $(R,\mathfrak{m})$ pseudo-Hens …
- 1,499
1
vote
1
answer
271
views
Local analyticity of volumes of slices of semi-algebraic sets
I would like a reference and/or a simple proof using well-known results of the following, which I think is true. (If it's false, I'd like to know that as well of course -- and ideally a way to modify …
- 1,499