Bjorn Poonen

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Polynomial representing all nonnegative integers

nt.number-theory polynomials open-problem asked Dec 25, 2009 at 6:40

mathoverflow.net

63 votes

Smooth proper scheme over Z

ag.algebraic-geometry nt.number-theory asked Dec 23, 2009 at 1:21

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47 votes

Collapsible group words

gr.group-theory co.combinatorics asked Feb 15, 2010 at 5:23

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46 votes

Strong induction without a base case

co.combinatorics examples mathematics-education lo.logic proof-theory asked Jan 16, 2010 at 6:16

mathoverflow.net

45 votes

Determinant of a determinant

linear-algebra matrices asked Oct 31, 2014 at 16:34

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40 votes

Do compact complex manifolds fall into countably many families?

complex-geometry asked May 1, 2017 at 22:18

mathoverflow.net

33 votes

Is the group of integer points on a finite-type group scheme over Z finitely presented?

arithmetic-geometry nt.number-theory algebraic-groups asked Apr 28, 2010 at 2:42

mathoverflow.net

26 votes

Is every curve birational to a smooth affine plane curve?

algebraic-curves ag.algebraic-geometry asked Dec 24, 2009 at 3:40

mathoverflow.net

21 votes

Does every relative curve have a Picard scheme?

ag.algebraic-geometry schemes picard-group asked Nov 10, 2014 at 13:46

mathoverflow.net

Top Answers

106

Conceptual reason why the sign of a permutation is well-defined?

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Experimental mathematics leading to major advances

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Is there an "elementary" proof of the infinitude of completely split primes?

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Polynomial with the primes as coefficients irreducible?

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How can I define the product of two ideals categorically?

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Expected determinant of a random NxN matrix

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Intuition for the last step in Serre's proof of the three-squares theorem

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Roots of truncations of $ e^x - 1$

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Bringing Number and Graph Theory Together: A Conjecture on Prime Numbers

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Order of the Tate-Shafarevich group

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When a formal power series is a rational function in disguise

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non principally polarized complex abelian varieties

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Is there a Whitney theorem type theorem for projective schemes?

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What's the probability that k + n^2 is squarefree, for fixed k?

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Integer matrices with no integer eigenvalues

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Are there any nonlinear solutions to $f(x+1) - f(x) = f'(x)$?

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Is a universally closed morphism of schemes quasi-compact ?

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What are interesting families of subsets of a given set?

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Theorems with unexpected conclusions

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Everywhere locally isomorphic abelian varieties

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Is a 'generic' variety nonsingular? Or singular?

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When f(x)-a and f(x)-b yield the same field extension

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Are most cubic plane curves over the rationals elliptic?

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Example of a smooth morphism where you can't lift a map from a nilpotent thickening?

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Is the theory of categories decidable?

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Size of the smallest group not satisfying an identity.

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Images of action of Galois on the Tate module of Elliptic Curve,

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Is there a matrix C so that the trace of C^n is dense in R?

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Least number of non-zero coefficients to describe a degree n polynomial

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When does a p-adic function have a Mahler expansion?

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