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NTHRYS › PhD Assistance › Algebra Number Theory

Algebra Number Theory

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Algebra Number Theory

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Elliptic Curves and Rational Points
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Modular Forms and L-functions
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Galois Theory and Field Extensions
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Diophantine Equations and Integer Solutions
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Arithmetic Algebraic Geometry
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p-adic Analysis and Hensel Lifting
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Homological Algebra and Derived Categories
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Representation Theory of Finite Groups
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Iwasawa Theory and Cyclotomic Fields
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Computational Number Theory Algorithms
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Class Field Theory Extensions
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Transcendental Number Theory
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Lattices and Integer Programming
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Commutative Ring Theory
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Algebraic K-theory and Cohomology
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Abelian Varieties and Jacobians
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Automorphic Forms and Langlands Program
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Quadratic Forms and Integer Matrices
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Cryptographic Number Theory Applications
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Zeta Functions and Analytic Methods
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Local Fields and Ramification Theory
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Noncommutative Algebra and Division Rings
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Primes in Arithmetic Progressions
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Algebraic Integers and Norms
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Polynomial Factorization Over Finite Fields
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Arithmetic Progressions and Additive Combinatorics
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Shimura Varieties and Hecke Correspondences
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Valuations and Absolute Values
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Frobenius Elements and Chebotarev Density
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Gorenstein Rings and Cohen-Macaulay Properties
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Biquadratic and Cyclic Field Extensions
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Baker Theory and Linear Forms in Logarithms
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Cyclotomic Units and Stickelberger Elements
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Intersection Theory on Algebraic Varieties
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Arithmetic of Hyperelliptic Curves
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Perfectoid Spaces and Tilting
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Ring Extensions and Integral Closures
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Dirichlet Characters and Gauss Sums
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Algebraic Cohomology Theories
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Pell Equations and Continued Fractions
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Class Number Computations and Tables
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Toric Varieties and Lattice Polytopes
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Group Cohomology and Extensions
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Selmer Groups and Descent Theory
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Henselian Rings and Strict Henselization
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Arithmetic Dynamics and Arithmetic Heights
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Sieve Methods in Algebraic Contexts
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Algebraic Deformation Theory
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Heights and Arithmetic Complexity
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Totality of Quadratic Residues
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Birational Geometry and Rational Maps
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Conductor and Discriminant Theory
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Tate Conjectures and Hodge Structures
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Witt Vectors and Teichmüller Theory
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Mahler Measures and Dynamical Systems
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Cohen-Lenstra Heuristics and Statistics
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Trace Formulas and Spectral Theory
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Stark Conjectures and Regulators
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Torsion Points on Abelian Varieties
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Fontaine-Laffaille Theory
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Gross-Zagier Formula Extensions
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Arakelov Geometry and Heights
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Brauer Groups and Cohomology
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Cyclotomic Abelian Varieties
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Thue-Siegel-Roth Diophantine Approximation
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Explicit Reciprocity Laws
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Kodaira-Spencer and Deformation Spaces
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Universal Norms and Circular Units
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Modular Jacobians and Rational Points
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Ostrowski Valuations and Extensions
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Sato-Tate Distributions
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Green Functions and Arithmetic Curves
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Generalized Fermat Equations
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Module Theory Over Orders
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Rational Preperiodic Points
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Satake Parameters and Functoriality
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Unramified Cohomology
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Primitive Roots and Artin Conjecture
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Rigid Analytic Geometry
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Picard Curves and Hyperelliptic Jacobians
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Wieferich and Wilson Primes
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Integral Points on Curves Algorithms
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Berkovich Spaces and Non-Archimedean Geometry
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Fitting Ideals and Determinants
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ABC Conjecture and Radical Bounds
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Geometric Invariant Theory
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Gross-Hopkins Duality
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Norm Subgroups and Ray Class Fields
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Elliptic Units and Special Values
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Quaternion Algebras and Orders
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Rank Bounds for Abelian Varieties
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Radical and Jacobson Rings
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Atiyah-Segal Completion Theorem
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Genus Theory and Binary Forms
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Exponential Diophantine Equations
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Lubin-Tate Formal Groups
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Toric Singularities and Resolutions
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Manin-Mumford Conjecture
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Depth Functions and Colength
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Analytic Continuation of Zeta Functions
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Arithmetic Surfaces and Effective Bounds
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Motivic Integration and Arc Spaces
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Derived Algebraic Geometry Methods
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Genus Curves and Jacobian Isogenies
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Algebraic Function Fields Arithmetic
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Monsky-Washnitzer Cohomology Theory
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Vertex Algebras and Number Theory
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Arithmetic Okounkov Bodies
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Equivariant Arakelov Geometry
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Sato-Tate Conjectures Beyond Curves
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Syntomic Cohomology and Applications
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Unlikely Intersections and Heights
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Arithmetic of CM Abelian Varieties
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Non-Abelian Chabauty Methods
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Sparse Polynomial Systems Solving
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Motivic Cohomology and Bloch-Kato
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Arithmetic Fundamental Groups Galois
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Generalized Jacobian Varieties
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Hasse-Davenport Relations Generalizations
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Integral Points on Surfaces Methods
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Quantum Invariants Number Theory
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Birch-Swinnerton-Dyer Conjecture Cases
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Refined Class Numbers and Iwasawa
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Toric Variety Zeta Functions
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Langlands Functoriality Bases
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Arithmetic Mirror Symmetry Correlates
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Moduli Spaces Integral Points
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Densities of Primes Number Fields
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Arithmetic Quantum Unique Ergodicity
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Rigid Analytic Varieties Geometry
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Hall Algebras Quantum Groups
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Ramification Fields and Bounds
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Definability and Decidability Problems
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Lattice Point Enumeration Algorithms
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Deligne Cohomology Arithmetic
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Quaternion Orders and Ideal Classes
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Frobenius Distributions Varieties
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Transcendence Theory Multiple Values
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Integral Canonical Models Shimura
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Arithmetic Satake Isomorphism
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Galois Covers and Dessin Interpretation
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Effective Isomorphism Testing Curves
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Mahler Measures and Heights
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Arithmetic Chow Groups Intersection
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Modular Curves Higher Genus
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Cluster Algebras Number Theory
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Berkovich Spaces Reduction Theory
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Supersingular Isogeny Cryptography
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Discriminant Bounds Discriminant Forms
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Perfectoid Geometry and Adic Spaces
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Birational Geometry and Minimal Models
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Derived Algebraic Geometry Foundations
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Arakelov Geometry and Heights
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Motivic Cohomology and Cycle Classes
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Étale Cohomology and Torsion
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Universal Coverings of Algebraic Curves
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Anabelian Geometry and Grothendieck Conjecture
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Rational Points on Fano Varieties
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Integral Points on Affine Varieties
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Ax-Grothendieck and Model Theory
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Unlikely Intersections and Unlikely Pairs
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Berkovich Analytic Geometry Dynamics
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Rational Canonical Forms and Invariants
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Central Simple Algebras and Brauer Groups
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Quaternion Algebras and Ternary Forms
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Lattice Points in Polyhedra Estimation
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Effective Diophantine Approximation Bounds
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Mahler Measure and Symmetric Functions
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Cyclotomic Extensions and Kummer Theory
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Catalan and Pillai Conjecture Approaches
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Elliptic Divisibility Sequences Dynamics
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Thue-Mahler and Generalized Exponential Equations
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Fermat Curves and Generalized Fermat Equations
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Modularity Lifting and Deformation Theory
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p-adic Hodge Theory and Crystalline Representations
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Bloch-Kato Exponential and L-values
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Fine Selmer Groups and Kolyvagin Methods
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Iwasawa Main Conjecture Generalizations
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Hida Families and Eigenvalue Variations
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Anti-cyclotomic Iwasawa Theory
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Overconvergent Modular Symbols
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L-invariants and Exceptional Cases
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Gross-Zagier Type Formulas Generalizations
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Stark Units and Stickelberger Class Relations
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Galois Cohomology and Descent Obstructions
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Chow Groups and Abel-Jacobi Mappings
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Hodge Theory and Period Domains
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Crystalline Cohomology and de Rham Theory
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Syntomic Cohomology and p-adic Comparison
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Prismatic Cohomology and Six Functors
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Character Sums and Kloosterman Sums
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Exponential Sums and Deligne Estimates
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Weil Conjectures and Etale Homology
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Arithmetic Codes and Algebraic Geometry
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Arithmetic Cryptography Pairing-based Schemes
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Post-Quantum Lattice-based Cryptography
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Arithmetic Boolean Circuits and Complexity
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Distribution of Primes in Special Sequences
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Generalized Riemann Hypothesis Consequences
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Perfectoid Spaces and Tilting Theory
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