21 citations · 47 across the 19 of their papers we have counts for
26 papers
Conductor-Discriminant Inequality for Tamely Ramified Cyclic Covers I
Andrew Obus, Padmavathi Srinivasan, Connor Stewart
We prove conductor-discriminant inequalities for all -covers of defined over discretely valued fields with excellent valuation ring …
Minimal regular normal crossings models of superelliptic curves
Andrew Obus, Padmavathi Srinivasan
Let be a complete discretely valued field with perfect residue field . If is a -cover with , we compute the mini…
Stabilization indices of potentially Mumford curves
Andrew Obus, Daniele Turchetti
Let be a smooth projective curve over a complete discretely valued field . Let be the minimal extension such that has a semi-stable model, and write $e(…
Explicit minimal embedded resolutions of divisors on models of the projective line
Andrew Obus, Padmavathi Srinivasan
Let be a discretely valued field with ring of integers with perfect residue field. Let be the rational function field in one variable. Let $\mathbb{P}^1_…
Superelliptic curves with many automorphisms and CM Jacobians
Andrew Obus, Tony Shaska
Let be a smooth, projective, genus curve, defined over . Then has \emph{many automorphisms} if its corresponding moduli point $p \…
Local Oort groups and the isolated differential data criterion
Huy Dang, Soumyadip Das, Kostas Karagiannis +2
It is conjectured that if k is an algebraically closed field of characteristic p > 0, then any branched G-cover of smooth projective k-curves where the "KGB" obstruction vanishes a…
Conductor-discriminant inequality for hyperelliptic curves in odd residue characteristic
Andrew Obus, Padmavathi Srinivasan
We prove an inequality between the conductor and the discriminant for all hyperelliptic curves defined over discretely valued fields with perfect residue field of characteristi…
Explicit resolution of weak wild quotient singularities on arithmetic surfaces
Andrew Obus, Stefan Wewers
A weak wild arithmetic quotient singularity arises from the quotient of a smooth arithmetic surface by a finite group action, where the inertia group of a point on a closed charact…
The Conjecture implies the Weak Diversity Conjecture
Hilaf Hasson, Andrew Obus
We show that the abc Conjecture implies the Weak Diversity Conjecture of Bilu and Luca.
Lifting of curves with automorphisms
Andrew Obus
The lifting problem for curves with automorphisms asks whether we can lift a smooth projective characteristic p curve with a group G of automorphisms to characteristic zero. This w…
Reduction of dynatomic curves
John R. Doyle, Holly Krieger, Andrew Obus +3
The dynatomic modular curves parametrize polynomial maps together with a point of period . It is known that the dynatomic curves are smooth and irreducible in character…
The local lifting problem for A_4
Andrew Obus
We solve the local lifting problem for the alternating group A_4, thus showing that it is a local Oort group. Specifically, if k is an algebraically closed field of characteristic…
Wild ramification kinks
Andrew Obus, Stefan Wewers
Given a branched cover between smooth projective curves over a non-archimedian mixed-characteristic local field and an open rigid disk , we study the questio…
A generalization of the Oort Conjecture
Andrew Obus
The Oort conjecture (now a theorem of Obus-Wewers and Pop) states that if k is an algebraically closed field of characteristic p, then any cyclic branched cover of smooth projectiv…
Abhyankar's conjectures in Galois theory: Current status and future directions
David Harbater, Andrew Obus, Rachel Pries +1
In this paper, we survey the major contributions of Abhyankar to the development of the theory of fundamental groups and Galois covers in positive characteristic. We first discuss…
Unramified Brauer classes on cyclic covers of the projective plane
Colin Ingalls, Andrew Obus, Ekin Ozman +1
Let X --> P^2 be a p-cyclic cover branched over a smooth, connected curve C of degree divisible by p, defined over a separably closed field of prime-to-p characteristic. We show th…
Good reduction of three-point Galois covers
Andrew Obus
Michel Raynaud gave a criterion for a three-point G-cover f : Y \rightarrow X = P^1, defined over a p-adic field K, to have good reduction. In particular, if the order of a p-Sylow…
Cyclic Extensions and the Local Lifting Problem
Andrew Obus, Stefan Wewers
The local Oort conjecture states that, if G is cyclic and k is an algebraically closed field of characteristic p, then all G-extensions of k[[t]] should lift to characteristic zero…
Conductors of wild extensions of local fields, especially in mixed characteristic (0,2)
Andrew Obus
If K_0 is the fraction field of the Witt vectors over an algebraically closed field k of characteristic p, we calculate upper bounds on the conductor of higher ramification for (th…
On Colmez's product formula for periods of CM-abelian varieties
Andrew Obus
Colmez conjectured a product formula for periods of abelian varieties with complex multiplication by a field K, analogous to the standard product formula in algebraic number theory…
The (local) lifting problem for curves
Andrew Obus
The lifting problem that we consider asks: given a smooth curve in characteristic p and a group of automorphisms, can we lift the curve, along with the automorphisms, to characteri…
Toward Abhyankar's Inertia Conjecture for PSL_2(\ell)
Andrew Obus
For \ell \neq p odd primes, we examine PSL_2(\ell)-covers of the projective line branched at one point over an algebraically closed field of characteristic p, where PSL_2(\ell) has…
Fields of moduli of three-point G-covers with cyclic p-Sylow, II
Andrew Obus
We continue the examination of the stable reduction and fields of moduli of G-Galois covers of the projective line over a complete discrete valuation field of mixed characteristic…
Fields of moduli of three-point G-covers with cyclic p-Sylow, I
Andrew Obus
We examine in detail the stable reduction of Galois covers of the projective line over a complete discrete valuation field of mixed characteristic (0, p), where G has a cyclic p-Sy…