Zobrazeno 1 - 10
of 138
pro vyhledávání: '"Bjorn Poonen"'
Publikováno v:
Forum of Mathematics, Sigma, Vol 4 (2016)
We introduce a common generalization of essentially all known methods for explicit computation of Selmer groups, which are used to bound the ranks of abelian varieties over global fields. We also simplify and extend the proofs relating what is comput
Externí odkaz:
https://doaj.org/article/6bf9cc0ada4e46a3bcb591d3718cef3d
Autor:
Bjorn Poonen
Publikováno v:
Arithmetic, Geometry, Cryptography, and Coding Theory 2021. :167-186
Our goal is to introduce Drinfeld modules and to explain their application to explicit class field theory.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2332218f0b9d909a0216940f7584177d
https://doi.org/10.1090/conm/779/15675
https://doi.org/10.1090/conm/779/15675
Autor:
Bjorn Poonen, Kaloyan Slavov
Publikováno v:
Bulletin of the London Mathematical Society, 54 (4)
Let G$G$ be a subgroup of the symmetric group Sn$S_n$. If the proportion of fixed-point-free elements in G$G$ (or a coset) equals the proportion of fixed-point-free elements in Sn$S_n$, then G=Sn$G=S_n$. The analogue for An$A_n$ holds if n > 7$n \geq
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0f5e744071770f39f602d14c00dc1337
https://hdl.handle.net/20.500.11850/544180
https://hdl.handle.net/20.500.11850/544180
Autor:
Bjorn Poonen, Sergey Rybakov
Publikováno v:
Proceedings of the National Academy of Sciences of the United States of America
Refining a theorem of Zarhin, we prove that given a $g$-dimensional abelian variety $X$ and an endomorphism $u$ of $X$, there exists a matrix $A \in \operatorname{M}_{2g}(\mathbb{Z})$ such that each Tate module $T_\ell X$ has a $\mathbb{Z}_\ell$-basi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cf375733e08377f94e1cf6618413c6e8
http://arxiv.org/abs/2107.06363
http://arxiv.org/abs/2107.06363
Autor:
Bjorn Poonen
Publikováno v:
Arithmetic Geometry, Number Theory, and Computation ISBN: 9783030809133
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fac0bd29848363bed48bc8fa3f1fcbc4
https://doi.org/10.1007/978-3-030-80914-0_21
https://doi.org/10.1007/978-3-030-80914-0_21
Let $E$ be an elliptic curve, with identity $O$, and let $C$ be a cyclic subgroup of odd order $N$, over an algebraically closed field $k$ with $\operatorname{char} k \nmid N$. For $P \in C$, let $s_P$ be a rational function with divisor $N \cdot P -
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a1a00a73e8ba5ea3562ba10602c4c7d3
https://www.repository.cam.ac.uk/handle/1810/325259
https://www.repository.cam.ac.uk/handle/1810/325259
Autor:
Bjorn Poonen
In 1922, Mordell conjectured the striking statement that for a polynomial equation $f(x,y)=0$, if the topology of the set of complex number solutions is complicated enough, then the set of rational number solutions is finite. This was proved by Falti
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b7bab89835c7890e6e0fbdcc41da958a
http://arxiv.org/abs/2006.01774
http://arxiv.org/abs/2006.01774
Autor:
Manjul Bhargava, Bjorn Poonen
We construct a stacky curve of genus $1/2$ (i.e., Euler characteristic $1$) over $\mathbb{Z}$ that has an $\mathbb{R}$-point and a $\mathbb{Z}_p$-point for every prime $p$ but no $\mathbb{Z}$-point. This is best possible: we also prove that any stack
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1dc3278bfa3938eb7096e075f324d171
http://arxiv.org/abs/2006.00167
http://arxiv.org/abs/2006.00167
Publikováno v:
MIT web domain
Tunisian J. Math. 2, no. 2 (2020), 287-307
Tunisian J. Math. 2, no. 2 (2020), 287-307
For each odd prime $p$, we conjecture the distribution of the $p$-torsion subgroup of $K_{2n}(\mathcal{O}_F)$ as $F$ ranges over real quadratic fields, or over imaginary quadratic fields. We then prove that the average size of the $3$-torsion subgrou
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a521a5393d4d4e1c199741683cc362f4
https://hdl.handle.net/1721.1/136644
https://hdl.handle.net/1721.1/136644
Autor:
Kaloyan Slavov, Bjorn Poonen
Publikováno v:
MIT web domain
We introduce a novel approach to Bertini irreducibility theorems over an arbitrary field, based on random hyperplane slicing over a finite field. Extending a result of Benoist, we prove that for a morphism $\phi \colon X \to \mathbb{P}^n$ such that $
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::aa9a9bc832e6091cecfe0a25fc6691cd
https://hdl.handle.net/1721.1/135257
https://hdl.handle.net/1721.1/135257