Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves

Manjul Bhargava, Arul Shankar, Takashi Taniguchi, Frank Thorne, Jacob Tsimerman, Zhao Yang

Type: Article

Publication Date: 2020-08-26

Citations: 45

DOI: https://doi.org/10.1090/jams/945

View Publication

Locations

Journal of the American Mathematical Society - View
arXiv (Cornell University) - View - PDF
MPG.PuRe (Max Planck Society) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves	2017	Manjul Bhargava Arul Shankar Takashi Taniguchi Frank Thorne Jacob Tsimerman Yongqiang Zhao
+	The rank of elliptic curves with rational 2-torsion points over large fields	2005	Bo‐Hae Im
+	2-Selmer groups, 2-class groups and rational points on elliptic curves	2017	Chao Li
+	Integral points on elliptic curves and 3-torsion in class groups	2006	H. A. Helfgott Akshay Venkatesh
+	Torsion for CM elliptic curves defined over number fields of degree 2𝑝	2022	Abbey Bourdon Holly Paige Chaos
+	ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group	2021	Jürgen Klüners Jiuya Wang
+	2-Selmer groups of even hyperelliptic curves over function fields	2022	Dao Van Thinh
+ PDF Chat	On the class numbers of the fields of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math>-torsion points of certain elliptic curves over<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"><mml:mi mathvariant="double-struck">Q</mml:mi></mml:math>	2015	Fumio Sairaiji Takuya Yamauchi
+ PDF Chat	Typically bounding torsion on elliptic curves isogenous to rational 𝑗-invariant	2022	Tyler Genao
+	On $2$-Selmer groups and quadratic twists of elliptic curves	2020	Daniel Barrera Salazar Ariel Pacetti Gonzalo Tornaría
+	On the $2$-Selmer group of Jacobians of hyperelliptic curves	2023	Daniel Barrera Salazar Ariel Pacetti Gonzalo Tornaría
+	Heights of points on elliptic curves over ℚ	2021	Michael Griffin Ken Ono Wei‐Lun Tsai
+	Elliptic curves with 2-torsion contained in the 3-torsion field	2015	Julio Brau Nathan Jones
+ PDF Chat	Computation of the 2-rank of pure cubic fields	1978	H. Eisenbeis Gerhard Frey B. Ommerborn
+ PDF Chat	Prime torsion in the Brauer group of an elliptic curve	2023	Charlotte Ure
+	Average bounds for the $$\ell $$ ℓ -torsion in class groups of cyclic extensions	2018	Christopher Frei Martin Widmer
+ PDF Chat	A remark concerning 𝑚-divisibility and the discrete logarithm in the divisor class group of curves	1994	Gerhard Frey Hans-Georg Rück
+	Torsion of elliptic curves with rational 𝑗-invariant defined over number fields of prime degree	2021	Tomislav Gužvić
+	Bound on Torsion Points on Elliptic Curves over Number Fields	2019	Darshan Nasit
+	Bounds on the torsion subgroups of Néron–Severi groups	2020	Hyuk Jun Kweon

Works That Cite This (42)

Action	Title	Year	Authors
+ PDF Chat	Towards van der Waerden’s conjecture	2023	Sam Chow Rainer Dietmann
+	ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group	2021	Jürgen Klüners Jiuya Wang
+	On a conjecture for $\ell$-torsion in class groups of number fields: from the perspective of moments	2021	Lillian B. Pierce Caroline L. Turnage‐Butterbaugh Melanie Matchett Wood
+ PDF Chat	Averages and higher moments for the $$\ell $$-torsion in class groups	2020	Christopher Frei Martin Widmer
+	Counting extensions of number fields with Frobenius Galois group	2019	Harsh Mehta
+	Estimates for the number of rational points on simple abelian varieties over finite fields	2019	Borys Kadets
+ PDF Chat	The distribution of G-Weyl CM fields and the Colmez conjecture	2023	Adrian Barquero-Sanchez Riad Masri Frank Thorne
+ PDF Chat	Estimates for the number of rational points on simple abelian varieties over finite fields	2020	Borys Kadets
+ PDF Chat	Counting 3-dimensional algebraic tori over <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi mathvariant="double-struck">Q</mml:mi></mml:math>	2023	Jungin Lee
+ PDF Chat	On the distribution of Alexander polynomials in certain families of closed braids	2023	Anwesh Ray

Works Cited by This (23)

Action	Title	Year	Authors
+	Integral points on elliptic curves and 3-torsion in class groups	2006	H. A. Helfgott Akshay Venkatesh
+ PDF Chat	Lectures on the geometry of numbers	1990	K. Chandrasekharan
+	Densities of quartic fields with even Galois groups	2005	Siman Wong
+	Integral Points on Elliptic Curves and the Bombieri-Pila Bounds	2013	Dave Mendes da Costa
+	The number of integral points on arcs and ovals	1989	Enrico Bombieri Jonathan Pila
+ PDF Chat	The density of abelian cubic fields	1954	Harvey Cohn
+	Sur le nombre des points rationnels de hauteur borné des variétés algébriques	1990	Victor V. Batyrev Yu. I. Manin
+	Counting cubic extensions with given quadratic resolvent	2010	Henri Cohen Anna Morra
+	Automorphic forms on GL(2) and the rank of class groups	1999	S.K Wong
+ PDF Chat	On the number of cubic orders of bounded discriminant having automorphism group <i>C</i><sub>3</sub>, and related problems	2014	Manjul Bhargava Ariel Shnidman