All Questions
Tagged with conjectures ag.algebraic-geometry
12 questions
3
votes
0
answers
193
views
Are local complete intersections of small codimension necessarily (global) complete intersections?
Hartshorne's 1974 conjecture states that a smooth closed subvariety $X$ of $\mathbb{CP}^r$ of dimension $>2/3r$ is necessarily (globally) a complete intersection. Is anything interesting known ...
- 16.9k
21
votes
1
answer
975
views
Conjecture: Given any five points, we can always draw a pair of non-intersecting circles whose diameter endpoints are four of those points
The following question resisted attacks at Math SE, so I thought I would try posting it here.
Is the following conjecture true or false:
Given any five coplanar points, we can always draw at least ...
- 3,527
28
votes
3
answers
5k
views
Why to believe the Fargues geometrization conjecture?
In the study of the arithmetic local Langlands correspondence, there is a conjecture that was recently (in this decade) formulated by Fargues.
I can't even concisely state the conjecture so I will ...
user140765
18
votes
1
answer
2k
views
Conjecture: The number of points modulo $p$ of certain elliptic curve is $p$ or $p+2$ for $p$ of form $p=27a^2+27a+7$
Numerical evidence suggests a conjecture that the number of
points of certain elliptic curve over $\mathbb{F}_p$ is
either $p$ or $p+2$ for $p$ of certain form.
Let $p$ be prime of the form $p=27a^2+...
- 25.4k
12
votes
2
answers
556
views
Sylvester–Gallai theorem with circle version, plane version and curve version?
The Sylvester–Gallai theorem in geometry states that, given a finite number of points in the Euclidean plane, either
All the points are collinear; or
There is a line which contains exactly two of the ...
- 477
18
votes
1
answer
1k
views
Which motivic cohomology groups of complex numbers are non-torsion?
I would like to know which motivic cohomology groups of complex numbers are non-zero and ("better") non-torsion, i.e., for which $(i,j)$ the $i$th cohomology of the complex ${\mathbb{Q}}(j)$ over $\...
- 16.9k
4
votes
1
answer
684
views
A problem of four curves
This is a generalization of my previous question, a problem of a cubic and six conics.
Let a curve $(K)$ of degree $m$ and three curves $(C_i)$ of degree $n$, for $i=1,2,3$. Let $(C_1)$ meets $(K)$ ...
- 1,044
15
votes
1
answer
732
views
A cubic and six conics problem
I am an electrical engineer system. I live in Viet Nam. I am not a Mathematician. I construct and found a problem as follows:
Let a cubic, and five conics $(C_1)$, $(C_2)$, $(C_3)$, $(C_4)$, $(C_5)$. ...
- 1,044
4
votes
0
answers
416
views
What is behind the Hodge conjecture? [duplicate]
My question is quite naive, and my knowledge limited on the subject. I heard lot of talks about Hodge conjecture. I wanted to ask about an intuitive way to figure out why we should care about Hodge ...
- 235
5
votes
1
answer
365
views
A conjecture associated with n-gon cut curve of degree m
This conjecture is a generalization of A theorem for cubic-A generalization of Carnot theorem, in MSE question. I'm an electrical engineer, I am not a mathematician. I don't know how to prove this ...
- 1,044
4
votes
1
answer
578
views
A conjecture like Cayley–Bacharach theorem
Let six points $A, A', B, B', C, C'$ lie on a conic and a cubic. Let a conic through $B, B', C, C'$ and meets the cubic again at $A_1, A_2$. Let a conic through $C, C', A, A'$ and meets the cubic ...
- 1,044
8
votes
1
answer
380
views
Is the Tate conjecture known for etale covers of products of curves
Let $X$ be a (smooth projective geometrically connected) surface over a finitely generated field $k$. The Tate conjecture predicts that, for $l$ a prime number invertible in $k$, the Chern class map ...
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