Model theory and diophantine geometry
نویسندگان
چکیده
منابع مشابه
Model Theory and Diophantine Geometry
I discuss some recent applications of model theory to diophantinetype problems in algebraic geometry. I give the required background, as well as a sketch of the proofs.
متن کاملDiophantine geometry from model theory
With Hrushovski’s proof of the function field Mordell-Lang conjecture [13] the relevance of geometric stability theory to diophantine geometry first came to light. A gulf between logicians and number theorists allowed for contradictory reactions. It has been asserted that Hrushovski’s proof was simply an algebraic argument masked in the language of model theory. Another camp held that this theo...
متن کاملErratum to “ Model Theory and Diophantine Geometry ”
Our informal description of the modularity of a definable set X of Morley dimension and degree 1 should have been: “There is no n-dimensional definable family of definable subsets of X × X with n ≥ 2, each of Morley dimension and Morley degree 1 and with pairwise intersections finite” in place of “There should be no infinite definable family of definable subsets of X×X , each of Morley dimensio...
متن کاملGalois Theory and Diophantine geometry
To a large extent, the investigations to be brought up today arise from a curious inadequacy having to do with the arrow on the left. On the one hand, it is widely acknowledged that the theory of motives finds a strong source of inspiration in Diophantine geometry, inasmuch so many of the structures, conjectures, and results therein have as model the conjecture of Birch and Swinnerton-Dyer, whe...
متن کاملModel Theory and Diophantine Geometry Lectures 3 , 4 and 5
These notes continue the notes of Anand Pillay on model theory and diophantine geometry. In my lectures I describe a model theoretic approach to some analogues of the Mordell-Lang conjecture for Drinfeld modules. Many questions remain open and algebraic proofs along the lines of the proof of the Manin-Mumford conjecture described by Pillay may be possible. We discuss these questions and potenti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1997
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-97-00730-1