Point-counting and the Zilber-Pink conjecture / Jonathan Pila.
By: Pila, Jonathan [author.].
Material type:
TextSeries: Cambridge tracts in mathematics ; 228.Publisher: Cambridge ; New York, NY : Cambridge University Press, 2022Description: x, 254 pages; PDS 95.00 23 cms.Content type: text Media type: unmediated Carrier type: volumeISBN: 9781009170321; 9781009170314.Subject(s): Arithmetical algebraic geometry | Diophantine equations | Modular curves | Model theory | MATHEMATICS / Number TheoryAdditional physical formats: Online version:: Point-counting and the Zilber-Pink conjectureDDC classification: 516.3/5 Other classification: MAT022000 | Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|
| Book | Chennai Mathematical Institute General Stacks | 516.35 PIL (Browse shelf) | Available | 11135 |
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| 516.35 OLS Algebraic spaces and stacks / | 516.35 PAT Introduction to algebraic geometry and commutative algebra / | 516.35 PER Algebraic geometry : an introduction / | 516.35 PIL Point-counting and the Zilber-Pink conjecture / | 516.35 POO Rational points on varieties / | 516.35 POO Rational points on varieties / | 516.35 REV Affine maps, Euclidean motions and quadrics / |
Includes bibliographical references and indexes.
Point-counting -- Multiplicative Manin-Mumford -- Powers of the modular curve as Shimura varieties -- Modular André-Oort -- Point-counting and the André-Oort conjecture -- Model theory and definable sets -- O-minimal structures -- Parameterization and point-counting -- Better bounds -- Point-counting and Galois orbit bounds -- Complex analysis in O-minimal structures -- Schanuel's conjecture and Ax-Schanuel -- A formal setting -- Modular Ax-Schanuel -- Ax-Schanuel for Shimura varieties -- Quasi-periods of elliptic curves -- Sources -- Formulations -- Some results -- Curves in a power of the modular curve -- Conditional modular Zilber-Pink -- O-minimal uniformity -- Uniform Zilber-Pink.