The work of Barry Mazur
From MaRDI portal
Publication:6200322
DOI10.4171/icm2022/217MaRDI QIDQ6200322
Publication date: 22 March 2024
Published in: International Congress of Mathematicians (Search for Journal in Brave)
primeselliptic curvesknotsmodular curvesrational pointsIwasawa theorydeformation theorymodular formsFermat's last theoremEuler systemsGalois representationsEisenstein ideal\(p\)-adic \(L\)-functionseigencurvesSchoenflies conjecture
Cites Work
- Diophantine stability
- Rational families of 17-torsion points of elliptic curves over number fields
- Notes on étale cohomology of number fields
- Perturbations, deformations, and variations (and “near-misses") in geometry, physics, and number theory
- Relative modular symbols and Rankin-Selberg convolutions
- The Square-Free Sieve and the Rank of Elliptic Curves
- Derived Hecke Algebra for Weight One Forms
- Prime Numbers and the Riemann Hypothesis
- Nearly ordinary Galois deformations over arbitrary number fields
- Combinatorial Equivalence Versus Topological Equivalence
- Open Problems in Number Theory, collected by Barry Mazur
- About Hermann Weyl’s “Ramifications, old and new, of the eigenvalue problem”
- Selmer companion curves
- Local Flat Duality
- Frobenius and the Hodge filtration
- Uniformity of rational points
- Big fields that are not large
- Points of order 13 on elliptic curves
- On embeddings of spheres
- On embeddings of spheres
- On the van Kampen theorem
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- Controlling Selmer groups in the higher core rank case
- Refined class number formulas for \(\mathbb{G}_m\)
- Disparity in Selmer ranks of quadratic twists of elliptic curves
- The spin of prime ideals
- On the characteristic power series of the \(U\) operator
- Reading Bombelli
- Symmetric homology spheres
- Class fields of abelian extensions of \(\mathbb Q\)
- Values of \(p\)-adic \(L\)-functions and a \(p\)-adic Poisson kernel
- On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer
- Growth of Selmer rank in nonabelian extensions of number fields
- Ranks of twists of elliptic curves and Hilbert's tenth problem
- Refined conjectures of the ``Birch and Swinnerton-Dyer type
- On the modular representations of degree two of \(\text{Gal}({\overline {\mathbb Q}}/{\mathbb Q})\)
- On the arithmetic of special values of L functions
- Galois representations, Kähler differentials and ``main conjectures
- Universal extensions and one dimensional crystalline cohomology
- Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
- Modular curves and the Eisenstein ideal
- Studying the growth of Mordell-Weil
- Visualizing elements of order three in the Shafarevich-Tate group
- Torsion points on elliptic curves and \(q\)-coefficients of modular forms
- On modular representations of \(\text{Gal}(\overline{\mathbb Q}/\mathbb Q)\) arising from modular forms
- The \(p\)-adic sigma function
- Arithmetic of Weil curves
- Modular elliptic curves and Fermat's Last Theorem
- Searching for \(p\)-adic eigenfunctions
- Bounds for the torsion of elliptic curves over number fields
- Beppo Levi and the arithmetic of elliptic curves
- An ``infinite fern in the universal deformation space of Galois representations
- Hypersurfaces of low degree
- Is it plausible?
- Explicit Chabauty-Kim for the split Cartan modular curve of level 13
- Computation of \(p\)-adic heights and log convergence
- Twisting commutative algebraic groups
- On periodic points
- A note on some contractible 4-manifolds
- The method of infinite repetition in pure topology. I
- The Iwasawa Main Conjectures for \(\mathrm{GL}_{2}\)
- Finding large Selmer rank via an arithmetic theory of local constants
- Finding large Selmer groups
- The method of infinite repetition in pure topology. II: Stable applications
- Differential topology from the point of view of simple homotopy theory
- Etale homotopy
- Local Euler characteristics
- Rational points of finite order on elliptic curves
- Rational points of Abelian varieties with values in towers of number fields
- Frobenius and the Hodge filtration (estimates)
- Organizing the arithmetic of elliptic curves
- Relative neighborhoods and the theorems of Smale
- The definition of equivalence of combinatorial imbeddings
- On the structure of certain semi-groups of spherical knot classes
- Orthotropy and spherical knots
- The Iwasawa conjecture for totally real fields
- A Markov model for Selmer ranks in families of twists
- Refined class number formulas and Kolyvagin systems
- On the passage from local to global in number theory
- How can we construct abelian Galois extensions of basic number fields?
- Simple neighborhoods
- Stable equivalence of differentiable manifolds
- Analogies Between Function Fields and Number Fields
- Rational connectivity and sections of families over curves
- Average ranks of elliptic curves: Tension between data and conjecture
- Finding meaning in error terms
- Arithmetic Moduli of Elliptic Curves. (AM-108)
- Arithmetic on curves
- Torsion points on elliptic curves defined over quadratic fields
- Number Theory as Gadfly
- Families of Modular Eigenforms
- Smoothings of Piecewise Linear Manifolds. (AM-80)
- Formal groups arising from algebraic varieties
- Questions of decidability and undecidability in Number Theory
- Filtrations on the homology of algebraic varieties
- Evolutions, Symbolic Squares, and Fitting Ideals
- Kolyvagin systems
- Visualizing Elements in the Shafarevich—Tate Group
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