Appendix I A Finiteness Theorem for Picard Curves With Good Reduction (by J. Estrada-Sarlabous)

1995 ◽  
pp. 133-143 ◽  
Author(s):  
J. Estrada-Sarlabous
Keyword(s):  
Finiteness Theorem ◽  
Good Reduction ◽  
Picard Curves

scholarly journals Critically separable rational maps in families

2012 ◽  
Vol 148 (6) ◽  
pp. 1880-1896 ◽  
Author(s):  
Clayton Petsche
Keyword(s):  
Fixed Point ◽  
Elliptic Curves ◽  
Number Field ◽  
Rational Maps ◽  
Finiteness Theorem ◽  
Good Reduction ◽  
Rational Map ◽  
Arithmetic Complexity ◽  
Special Case

AbstractGiven a number field K, we consider families of critically separable rational maps of degree d over K possessing a certain fixed-point and multiplier structure. With suitable notions of isomorphism and good reduction between rational maps in these families, we prove a finiteness theorem which is analogous to Shafarevich’s theorem for elliptic curves. We also define the minimal critical discriminant, a global object which can be viewed as a measure of arithmetic complexity of a rational map. We formulate a conjectural bound on the minimal critical discriminant, which is analogous to Szpiro’s conjecture for elliptic curves, and we prove that a special case of our conjecture implies Szpiro’s conjecture in the semistable case.

scholarly journals Primes Dividing Invariants of CM Picard Curves

2019 ◽  
Vol 72 (2) ◽  
pp. 480-504 ◽  
Author(s):  
Pınar Kılıçer ◽  
Elisa Lorenzo García ◽  
Marco Streng
Keyword(s):  
Complex Multiplication ◽  
Good Reduction ◽  
Explicit Constructions ◽  
Picard Curves ◽  
Genus 2 ◽  
Reduction Of Curves

AbstractWe give a bound on the primes dividing the denominators of invariants of Picard curves of genus 3 with complex multiplication. Unlike earlier bounds in genus 2 and 3, our bound is based, not on bad reduction of curves, but on a very explicit type of good reduction. This approach simultaneously yields a simplification of the proof and much sharper bounds. In fact, unlike all previous bounds for genus 3, our bound is sharp enough for use in explicit constructions of Picard curves.

scholarly journals Picard curves over with good reduction away from 3

2016 ◽  
Vol 19 (2) ◽  
pp. 382-408 ◽  
Author(s):  
Beth Malmskog ◽  
Christopher Rasmussen
Keyword(s):  
Good Reduction ◽  
Binary Forms ◽  
Linear Factor ◽  
Isomorphism Classes ◽  
Picard Curves ◽  
Exhaustive List

Inspired by methods of N. P. Smart, we describe an algorithm to determine all Picard curves over $\mathbb{Q}$ with good reduction away from 3, up to $\mathbb{Q}$-isomorphism. A correspondence between the isomorphism classes of such curves and certain quintic binary forms possessing a rational linear factor is established. An exhaustive list of integral models is determined and an application to a question of Ihara is discussed.

scholarly journals $L^{p}$ harmonic 1-forms on conformally flat Riemannian manifolds

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jing Li ◽  
Shuxiang Feng ◽  
Peibiao Zhao
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Finiteness Theorem ◽  
Conformally Flat ◽  
Locally Conformally Flat ◽  
Flat Riemannian Manifold ◽  
Ricci Form

AbstractIn this paper, we establish a finiteness theorem for $L^{p}$ L p harmonic 1-forms on a locally conformally flat Riemannian manifold under the assumptions on the Schrödinger operators involving the squared norm of the traceless Ricci form. This result can be regarded as a generalization of Han’s result on $L^{2}$ L 2 harmonic 1-forms.

scholarly journals RAPOPORT–ZINK UNIFORMIZATION OF HODGE-TYPE SHIMURA VARIETIES

2018 ◽  
Vol 6 ◽  
Author(s):  
WANSU KIM
Keyword(s):  
Shimura Varieties ◽  
Good Reduction ◽  
Canonical Models

We show that the integral canonical models of Hodge-type Shimura varieties at odd good reduction primes admits ‘$p$-adic uniformization’ by Rapoport–Zink spaces of Hodge type constructed in Kim [Forum Math. Sigma6(2018) e8, 110 MR 3812116].

scholarly journals Torsion points of elliptic curves with good reduction

2008 ◽  
Vol 31 (3) ◽  
pp. 385-403
Author(s):  
Masaya Yasuda
Keyword(s):  
Elliptic Curves ◽  
Good Reduction ◽  
Torsion Points

A Finiteness Theorem for Meromorphic Mappings Sharing Few Moving Hyperplanes

2015 ◽  
Vol 43 (4) ◽  
pp. 725-742 ◽  
Author(s):  
Si Duc Quang ◽  
Ha Huong Giang
Keyword(s):  
Finiteness Theorem ◽  
Meromorphic Mappings

scholarly journals A Galois criterion for good reduction of τ-sheaves

2002 ◽  
Vol 97 (2) ◽  
pp. 447-471 ◽  
Author(s):  
Francis Gardeyn
Keyword(s):  
Good Reduction

scholarly journals Constructing elliptic curves from Galois representations

2018 ◽  
Vol 154 (10) ◽  
pp. 2045-2054
Author(s):  
Andrew Snowden ◽  
Jacob Tsimerman
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Galois Representations ◽  
Good Reduction ◽  
Arithmetic Surface

Given a non-isotrivial elliptic curve over an arithmetic surface, one obtains a lisse $\ell$-adic sheaf of rank two over the surface. This lisse sheaf has a number of straightforward properties: cyclotomic determinant, finite ramification, rational traces of Frobenius elements, and somewhere not potentially good reduction. We prove that any lisse sheaf of rank two possessing these properties comes from an elliptic curve.

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