Zobrazeno 1 - 10
of 40
pro vyhledávání: '"Philipp Habegger"'
Publikováno v:
Oberwolfach Reports. 19:1091-1164
Autor:
Philipp Habegger
Publikováno v:
ASA Bulletin. 38:548-579
Publikováno v:
International Mathematics Research Notices. 2021:1138-1159
Consider a one-parameter family of smooth, irreducible, projective curves of genus $g\ge 2$ defined over a number field. Each fiber contains at most finitely many rational points by the Mordell Conjecture, a theorem of Faltings. We show that the numb
Publikováno v:
Annals of Mathematics
Annals of Mathematics, Princeton University, Department of Mathematics, 2021, 194 (1), pp.237-298. ⟨10.4007/annals.2021.194.1.4⟩
Annals of Mathematics, Princeton University, Department of Mathematics, 2021, 194 (1), pp.237-298. ⟨10.4007/annals.2021.194.1.4⟩
International audience; Consider a smooth, geometrically irreducible, projective curve of genus g ≥ 2 defined over a number field of degree d ≥ 1. It has at most finitely many rational points by the Mordell Conjecture, a theorem of Faltings. We s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fe5743175c54810714cf926214a5144a
https://hal.sorbonne-universite.fr/hal-03374335
https://hal.sorbonne-universite.fr/hal-03374335
Publikováno v:
International Mathematics Research Notices
International Mathematics Research Notices, Oxford University Press (OUP), 2020, pp.10005-10041. ⟨10.1093/imrn/rny274⟩
International Mathematics Research Notices, Oxford University Press (OUP), 2020, pp.10005-10041. ⟨10.1093/imrn/rny274⟩
A result of the second-named author states that there are only finitely many CM-elliptic curves over $\mathbb{C}$ whose $j$-invariant is an algebraic unit. His proof depends on Duke's Equidistribution Theorem and is hence non-effective. In this artic
Publikováno v:
Duke Mathematical Journal
Duke Mathematical Journal, Duke University Press, 2021, 170 (2), pp.247-277. ⟨10.1215/00127094-2020-0044⟩
Duke Math. J. 170, no. 2 (2021), 247-277
Duke Mathematical Journal, 2021, 170 (2), pp.247-277. ⟨10.1215/00127094-2020-0044⟩
Duke Mathematical Journal, Duke University Press, 2021, 170 (2), pp.247-277. ⟨10.1215/00127094-2020-0044⟩
Duke Math. J. 170, no. 2 (2021), 247-277
Duke Mathematical Journal, 2021, 170 (2), pp.247-277. ⟨10.1215/00127094-2020-0044⟩
We prove the geometric Bogomolov conjecture over a function field of characteristic zero.
18 pages
18 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5cffa4f25bfeeda5f7e11504bdce4a81
https://hal.archives-ouvertes.fr/hal-02334181/document
https://hal.archives-ouvertes.fr/hal-02334181/document
Publikováno v:
Schweizerische Ärztezeitung.
Autor:
Su-Ion Ih, Philipp Habegger
Publikováno v:
Transactions of the American Mathematical Society. 371:357-386
Let $ K$ be a number field with algebraic closure $ \overline K$, and let $ S$ be a finite set of places of $ K$ containing all the infinite ones. Let $ {\it\Gamma }_0$ be a finitely generated subgroup of $ {\mathbb{G}}_{\textup {m}} (\overline K)$,
Autor:
Philipp Habegger
Publikováno v:
Selecta Mathematica. 24:1633-1675
Consider the vanishing locus of a real analytic function on $\mathbb{R}^n$ restricted to $[0,1]^n$. We bound the number of rational points of bounded height that approximate this set very well. Our result is formulated and proved in the context of o-
Autor:
Philipp Habegger, Fabien Pazuki
Publikováno v:
Compositio Mathematica. 153:2534-2576
We show that a genus $2$ curve over a number field whose jacobian has complex multiplication will usually have stable bad reduction at some prime. We prove this by computing the Faltings height of the jacobian in two different ways. First, we use a k