Chevalley-Warning, Beyond and Beneath by Pete L Clark
The Chevalley-Warning Theorem answers a fundamental question about a low degree polynomial system over a finite field: the number of solutions is divisible by the characteristic. Since its discovery in 1935, this result has become a powerful tool with applications across number theory, combinatorics, and theoretical computer science. This book explores the mathematics lying beyond and beneath the Chevalley-Warning Theorem. The first chapter goes beyond by treating stronger versions due to Ax-Katz (1964 and 1971) and Moreno-Moreno (1995), among others. By comparing multiple proofs of these classical results, the reader also learns what lies beneath them, uncovering a ""core mathematics"" that combines aspects of algebraic number theory, basic commutative algebra, combinatorics and interpolation theory but can be explored on its own terms. Further development of the mathematics underneath leads to generalizations of Chevalley-Warning (and beyond) to several other contexts: arbitrary finite rings, restricted variables and even to purely group-theoretic generalizations. The final chapter highlights applications of these ideas in additive combinatorics, discrete geometry, graph theory, and interpolation theory. With prerequisites limited to basic algebraic number theory, the book is particularly suitable for graduate students in number theory. At the same time, it will appeal to combinatorialists and to readers interested in modern developments of the polynomial method.-
Quantum Field Theory
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Non-Abelian Monopoles and Four-Manifold Topology
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Quantum Topology Via Modified Traces
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Abelian Varieties
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Combinatorial Factorization Theory
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Discrete Convex Analysis
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The Cremona Group and Its Subgroups
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Fokker-Planck-Kolmogorov Equations
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Grid Homology for Knots and Links
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The Classification of the Finite Simple Groups, Number 6
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The Classification of the Finite Simple Groups, Number 7
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Braid and Knot Theory in Dimension Four
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Residuated Structures in Algebra and Logic
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Attractors for Degenerate Parabolic Type Equations
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Advanced Analytic Number Theory: L-functions
- Geometric Function Theory in the Unit Ball of $\mathbb{C}^n$
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Cohen-Macaulay Representations
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The Convenient Setting of Global Analysis
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Noncommutative Multivariable Operator Theory
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Singular Time-Homogeneous Ito Equations and PDEs
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Locally Solid Riesz Spaces with Applications to Economics
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Control and Nonlinearity
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Mixed Motives
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Ergodic Theory Via Joinings
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Ricci Solitons in Dimensions $4$ and Higher
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Vertex Algebras and Algebraic Curves
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Surgery on Compact Manifolds
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Univalent Functions in Quantum Probability Theory
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Perfectoid Spaces
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The Ricci Flow: Techniques and Applications
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Parabolic Geometries I
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Trees of Hyperbolic Spaces
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Foundations of Arithmetic Differential Geometry
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Algebraic Geometry for Scientists and Engineers
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Operators, Functions, and Systems
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Mirror Symmetry and Algebraic Geometry
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Geometric Analysis on Symmetric Spaces
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Self-Similar Groups
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Knotted Surfaces and Their Diagrams
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Alice and Bob Meet Banach
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Weak Convergence of Measures
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Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups
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Iwasawa Theory and Its Perspective, Volume 1
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Discrete-Time Dynamics of Structured Populations and Homogeneous Order-Preserving Operators
Pete L. Clark, University of Georgia, Athens, GA
| SKU | Unavailable |
| ISBN 13 | 9781470484699 |
| ISBN 10 | 1470484692 |
| Title | Chevalley-Warning, Beyond and Beneath |
| Author | Pete L Clark |
| Series | Mathematical Surveys And Monographs |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | American Mathematical Society |
| Year published | 2026-09-01 |
| Number of pages | 454 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |