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Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
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Point-Counting and the Zilber-Pink Conjecture (Hardcover)
Loot Price: R2,908
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Point-Counting and the Zilber-Pink Conjecture (Hardcover)
Series: Cambridge Tracts in Mathematics
Expected to ship within 12 - 17 working days
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Point-counting results for sets in real Euclidean space have found
remarkable applications to diophantine geometry, enabling
significant progress on the Andre-Oort and Zilber-Pink conjectures.
The results combine ideas close to transcendence theory with the
strong tameness properties of sets that are definable in an
o-minimal structure, and thus the material treated connects ideas
in model theory, transcendence theory, and arithmetic. This book
describes the counting results and their applications along with
their model-theoretic and transcendence connections. Core results
are presented in detail to demonstrate the flexibility of the
method, while wider developments are described in order to
illustrate the breadth of the diophantine conjectures and to
highlight key arithmetical ingredients. The underlying ideas are
elementary and most of the book can be read with only a basic
familiarity with number theory and complex algebraic geometry. It
serves as an introduction for postgraduate students and researchers
to the main ideas, results, problems, and themes of current
research in this area.
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