Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options not deleted user 91041

Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

7 votes
1 answer
261 views

Explicit equations for the universal vector extension of an elliptic curve

The universal vector extension $E$ of an abelian variety $A$ is an algebraic group, an extension of $A$ by a vector group $0 \to V \to E \to A \to 0$, such that any other extension of $A$ by a vector …
Vik78's user avatar
  • 658
4 votes
1 answer
183 views

Jacobian criterion for Zariski cotangent space over arbitrary field (X-post from SE)

I apologize as I am certain this is not research-level, but several days have gone by without an answer on stackexchange (https://math.stackexchange.com/questions/4724245/jacobian-criterion-for-zarisk …
Vik78's user avatar
  • 658
4 votes
2 answers
316 views

Is the set of points on an abelian surface which project to rational points on the Kummer su...

Let $C$ be a hyperelliptic curve of genus 2 defined over $\mathbb{Q}$, let $J$ be its Jacobian, and let $X$ be the Kummer surface associated to $J$ (i. e. $X$ is the singular Kummer surface which resu …
Vik78's user avatar
  • 658
4 votes
1 answer
234 views

Known cases of Tate conjecture for varieties which are smooth over a curve

What are some examples of smooth projective varieties $X$ over a finite field for which the Tate conjecture for divisors is known, and which admit a smooth morphism to a smooth projective curve? I am …
Vik78's user avatar
  • 658
3 votes
Accepted

Deligne finitude and finiteness of etale cohomology

See the answers here: https://mathoverflow.net/questions/76069/finiteness-of-étale-cohomology-groups . Because $k$ is finite, a constructible sheaf on (Spec $k)_{et}$ has finite cohomology groups. Del …
Vik78's user avatar
  • 658
3 votes
0 answers
178 views

Wondering if Monsky-Washnitzer ever published a result claimed to be forthcoming in a later ...

At the very end of the paper Formal Cohomology I by Monsky and Washnitzer, they write the following: "In some sense, the operator $\psi$ applied to a power series gives it "better growth conditions". …
Vik78's user avatar
  • 658
3 votes
0 answers
80 views

Let $f: X \to D$ be a proper holomorphic submersion. Does a holomorphic form on $X$, closed ...

Let $D$ be the unit disc in $\mathbb{C}^n$ and let $f: X \to D$ be a proper surjective holomorphic submersion, which is trivial as a smooth fiber bundle, with connected fiber $F$. We get an induced fl …
Vik78's user avatar
  • 658
3 votes
Accepted

Zeta function of variety over positive characteristic function field vs. local zeta factor o...

The two zeta functions are the same. This is an immediate corollary of Milne, Etale Cohomology, proposition 13.8(c). Reference: Milne, J. S. Etale Cohomology (PMS-33). Princeton University Press, 1980 …
Vik78's user avatar
  • 658
3 votes
0 answers
62 views

Are motives of K3 surfaces of abelian type?

I refer to the article of van Geemen https://arxiv.org/pdf/math/9903146. What van Geemen calls the Kuga-Satake-Hodge conjecture suggests that for a K3 surface $X$ over $\mathbb{C}$, the summand $h^2(X …
Vik78's user avatar
  • 658
3 votes
0 answers
140 views

Tate conjecture for singular varieties in terms of intersection homology

In his book “Mixed motives and algebraic K-theory”, Jannsen generalizes the Tate conjecture to a potentially singular projective variety $X$ over a finitely generated field. The statement is the same …
Vik78's user avatar
  • 658
2 votes
1 answer
218 views

Looking for an example of a point $P$ on an abelian variety $X$ such that no curve on $X$ co...

Is there an example of an abelian variety $X$ defined over a number field $K$, with $\dim X > 1$, and a $K$-rational point $P$ on $X$, such that no curve $C$ on $X$ (say defined over a number field) c …
Vik78's user avatar
  • 658
2 votes
0 answers
35 views

Leray spectral sequence for étale homology

Let $X$, $Y$, $Z$ be quasi-projective varieties over an algebraically closed field $k$, $f: X \to Y$ and $g: Z \to X$ proper (even projective) maps with $f$ smooth, and $h: Z \to Y$ their composite. C …
Vik78's user avatar
  • 658
1 vote

Any irreducible projective curve in $\mathbb P^3$ can be defined by three functions

EDIT: this answer has some issues. See the comments. I think a similar line of reasoning shows you can do it with four equations, though. For reasons of dimension your curve is contained in a hypersur …
Vik78's user avatar
  • 658
1 vote

Does going-down theorem hold for local homomorphism of finite flat dimension?

Here's a counterexample with $A$ and $B$ of the same Krull dimension. Take $A = B = \mathbb{C}[x,y]_{(x,y)}$, and let $f: A \to B$ be the composition of the quotient of $A$ by $(y)$ with the embedding …
Vik78's user avatar
  • 658
1 vote
1 answer
158 views

Zeta function of variety over positive characteristic function field vs. local zeta factor o...

Let $X = Y \times_{\mathbb{F}_q} C$, with $Y, C / \mathbb{F}_q$ smooth projective varieties, $C$ a curve. Let $d = \dim_{\mathbb{F}_q} X$. We can consider the local zeta function $Z(X, t) = \prod\limi …
Vik78's user avatar
  • 658

15 30 50 per page