Zobrazeno 1 - 10
of 33
pro vyhledávání: '"Dogra, Netan"'
Autor:
Dogra, Netan
We give refined methods for proving finiteness of the Chabauty--Coleman--Kim set $X(\mathbb{Q}_2 )_2 $, when $X$ is a hyperelliptic curve with a rational Weierstrass point. The main developments are methods for computing Selmer conditions at $2$ and
Externí odkaz:
http://arxiv.org/abs/2403.07476
Autor:
Dogra, Netan
We give a proof of the Zilber--Pink conjecture for $n$-fold self-products of a curve $X$ inside the self-product of its Jacobian, when $X$ has appropriate bad reduction, its Jacobian has no extra endomorphisms, and $n$ is sufficiently small. The stra
Externí odkaz:
http://arxiv.org/abs/2403.05481
Autor:
Dogra, Netan
This paper introduces explicit Galois cohomological methods for determining the ranks of Bloch--Kato Selmer groups associated to the Tate twists of the 2-adic second \'etale cohomology of the Jacobian of a hyperelliptic curve with a rational Weierstr
Externí odkaz:
http://arxiv.org/abs/2312.04996
Autor:
Dogra, Netan
We prove that the set of `low rank' points on sufficiently large fibre powers of families of curves are not Zariski dense. The recent work of Dimitrov-Gao-Habegger and K\"uhne (and Yuan) imply the existence of a bound which is exponential in the rank
Externí odkaz:
http://arxiv.org/abs/2206.04304
We describe how the quadratic Chabauty method may be applied to explicitly determine the set of rational points on modular curves of genus $g>1$ whose Jacobians have Mordell--Weil rank $g$. This extends our previous work on the split Cartan curve of
Externí odkaz:
http://arxiv.org/abs/2101.01862
Autor:
Dogra, Netan
Results in $p$-adic transcendence theory are applied to two problems in the Chabauty-Coleman method. The first is a question of McCallum and Poonen regarding repeated roots of Coleman integrals. The second is to give lower bounds on the $p$-adic dist
Externí odkaz:
http://arxiv.org/abs/2008.09560
Autor:
Betts, L. Alexander, Dogra, Netan
We study the Galois action on paths in the $\mathbb{Q}_\ell$-pro-unipotent \'etale fundamental groupoid of a hyperbolic curve $X$ over a $p$-adic field with $\ell\neq p$. We prove an Oda--Tamagawa-type criterion for the existence of a Galois-invarian
Externí odkaz:
http://arxiv.org/abs/1909.05734
Autor:
Dogra, Netan, Fourn, Samuel Le
In this paper, we provide refined sufficient conditions for the quadratic Chabauty method to produce a finite set of points, with the conditions on the rank of the Jacobian replaced by conditions on the rank of a quotient of the Jacobian plus an asso
Externí odkaz:
http://arxiv.org/abs/1906.08751
Autor:
Dogra, Netan
The Chabauty--Kim method is a tool for finding the integral or rational points on varieties over number fields via certain transcendental $p$-adic analytic functions arising from certain Selmer schemes associated to the unipotent fundamental group of
Externí odkaz:
http://arxiv.org/abs/1903.05032
Autor:
Balakrishnan, Jennifer, Dogra, Netan
Publikováno v:
Compositio Math. 155 (2019) 1057-1075
The Chabauty--Kim method is a method for finding rational points on curves under certain technical conditions, generalising Chabauty's proof of the Mordell conjecture for curves with Mordell--Weil rank less than their genus. We show how the Chabauty-
Externí odkaz:
http://arxiv.org/abs/1803.10102