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Results tagged with ag.algebraic-geometry
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user 58688
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
1
vote
0
answers
386
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Pullback/pushforward of bivariant intersection classes
In chapter 17 of Fulton's Intersection Theory, he defines a bivariant intersection theory. I'm a bit puzzled by the pushforward/pullback he defines on page 322-323, though; they seem not analogous to …
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3
votes
Some questions about the map $K_0(\text{Var})\to K_0(\text{Mot})$
Answer to question #2 is no. (Also I don't know what I meant by "restrict to classes of smooth varieties" since these generate the ring in the only case where we know how to define the map.) $[\mathbb …
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8
votes
2
answers
784
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Some questions about the map $K_0(\text{Var})\to K_0(\text{Mot})$
Let $k$ be a field. The naive Grothendieck ring of varieties $K_0(\text{Var})$ is generated by isomorphism classes of varieties over $k$ with the scissors relation $[X]=[X-Y]+[Y]$ for $Y$ a closed sub …
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17
votes
2
answers
2k
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What does taking the graded algebra do to the Grothendieck group, and its relation to the Ch...
Let $X$ be a nonsingular variety. (Perhaps some/all of this works over more general smooth schemes, but let's stick to the simple case.)
In, e.g., Fulton's Intersection Theory chapter 15, and Soule's …
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6
votes
Deep/precise relationship between two approaches to FLT for polynomials, $n = 3$
I find it highly unlikely that the two proofs are really thematically linked in any way. The first, being an infinite descent proof, is in some sense doing geometry "over $\mathbb{C}[t]$" - in that on …
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6
votes
0
answers
297
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Overview and/or reference of theory of pro-universal covers?
This question will contain very little in the way of concrete information, because I don't have much to go on. I've heard whispers of something called a "pro-universal cover," which is the inverse lim …
- 693