scholarly journals On the characterizations of cofinite complexes over affine curves and hypersurfaces

2017 ◽  
Vol 479 ◽  
pp. 314-325
Author(s):  
Ken-ichiroh Kawasaki
Keyword(s):  
Affine Curves

scholarly journals Integer points on algebraic curves with exceptional units

1997 ◽  
Vol 63 (2) ◽  
pp. 145-164 ◽  
Author(s):  
Dimitrios Poulakis
Keyword(s):  
Elliptic Equations ◽  
Algebraic Curves ◽  
Irreducible Polynomial ◽  
Algebraic Number Field ◽  
Genus Zero ◽  
Integer Points ◽  
Regular Functions ◽  
Affine Curves ◽  
Absolutely Irreducible Polynomial ◽  
Integral Solutions

AbstractLet F(X, Y) be an absolutely irreducible polynomial with coefficients in an algebraic number field K. Denote by C the algebraic curve defined by the equation F(X, Y) = 0 and by K[C] the ring of regular functions on Cover K. Assume that there is a unit ϕ in K[C] − K such that 1 − ϕ is also a unit. Then we establish an explicit upper bound for the size of integral solutions of the equation F(X, Y) = 0, defined over K. Using this result we establish improved explicit upper bounds on the size of integral solutions to the equations defining non-singular affine curves of genus zero, with at least three points at ‘infinity’, the elliptic equations and a class of equations containing the Thue curves.

scholarly journals Affine curves on which every point is a set-theoretic complete intersection

1984 ◽  
Vol 87 (1) ◽  
pp. 113-135 ◽  
Author(s):  
Edward D Davis ◽  
Paolo Maroscia
Keyword(s):  
Complete Intersection ◽  
Affine Curves

scholarly journals Integral points of bounded degree on affine curves

2015 ◽  
Vol 152 (4) ◽  
pp. 754-768 ◽  
Author(s):  
Aaron Levin
Keyword(s):  
Number Field ◽  
Analogous Result ◽  
Complete Characterization ◽  
Integral Points ◽  
Bounded Degree ◽  
Holomorphic Map ◽  
Affine Curves ◽  
Picard’S Theorem ◽  
Picard's Theorem

We generalize Siegel’s theorem on integral points on affine curves to integral points of bounded degree, giving a complete characterization of affine curves with infinitely many integral points of degree $d$ or less over some number field. Generalizing Picard’s theorem, we prove an analogous result characterizing complex affine curves admitting a nonconstant holomorphic map from a degree $d$ (or less) analytic cover of $\mathbb{C}$.

A Note on Euclidean Rings of Affine Curves

1984 ◽  
Vol s2-29 (2) ◽  
pp. 229-236 ◽  
Author(s):  
M. L. Brown
Keyword(s):  
Affine Curves
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