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Results tagged with ag.algebraic-geometry
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user 7935
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
2
votes
1
answer
432
views
Is the tensor product of two acyclic sheaves on a scheme acyclic?
Ampleness and acyclicity are related; for example, large tensor powers of an ample sheaf are acyclic and the converse holds for line bundles. The tensor product of two ample sheaves is ample; this pro …
- 804
1
vote
2
answers
2k
views
Effect of tensor product on euler characteristic of line bundles
Suppose X is a curve.
Under sufficiently nice conditions we have that every line bundle on X corresponds to an equivalence class of divisors modulo principal divisors, with tensor product of bundles …
- 804
1
vote
0
answers
75
views
Closure of the set of principal ideals under a certain operation
Suppose $K$ is a field, and $R$ is the polynomial ring $K[x_1, \ldots, x_n]$.
Suppose $S$ is a set of ideals of $R$ satisfying these properties:
$S$ contains all principal ideals.
If $I$, $J$, and …
- 804
3
votes
1
answer
843
views
Tate's thesis for varieties over finite fields
Tate showed that the functional equation for zeta functions of number fields can be proven with fourier-analytic methods on the adele ring. Can the same be done for zeta functions of varieties over fi …
- 804
16
votes
Accepted
Are the ideles literally a Picard group?
As explained in the comments, I disagree with this analogy. Nonetheless, there is a way you can realize the idele class group (not the ideles) as a group of line-bundle-like objects under the tensor p …
- 804
5
votes
1
answer
406
views
Rationality of trace of endomorphism of Iwasawa-thing
Let $n$ be a positive integer, and $p$ a prime number. Let $K_i$ be the cyclotomic field containing exactly the $np^i$th roots of unity. Let $H$ be the inverse limit of $p$-power torsion of the class …
- 804