80 citations · 218 across the 21 of their papers we have counts for
23 papers
Ogg's Torsion conjecture: Fifty years later
Jennifer S. Balakrishnan, Barry Mazur
Andrew Ogg's mathematical viewpoint has inspired an increasingly broad array of results and conjectures. His results and conjectures have earmarked fruitful turning points in our s…
Derived class field theory
Tony Feng, Michael Harris, Barry Mazur
We sketch the construction of a derived enhancement of the reciprocity isomorphism of class field theory. Details will appear in a forthcoming joint paper of the authors with A. Ra…
Defining using unit groups
Barry Mazur, Karl Rubin, Alexandra Shlapentokh
We consider first-order definability and decidability questions over rings of integers of algebraic extensions of $\Q$, paying attention to the uniformity of definitions. The unifo…
Existential definability and diophantine stability
Barry Mazur, Karl Rubin, Alexandra Shlapentokh
Let be a number field, let be an algebraic (possibly infinite degree) extension of , and let be their rings of integers. Suppose is an abelian…
Corrections to {\it Uniformity of rational points} and further comments
Lucia Caporaso, Joe Harris, Barry Mazur
This paper corrects an error in the authors' earlier work, by proving stronger forms of the basic lemmas
Big fields that are not large
Barry Mazur, Karl Rubin
A subfield of is if every smooth curve over with a rational point has infinitely many rational points. A subfield of i…