<p>This exploration of the relation between periods and transcendental numbers brings Baker's theory of linear forms in logarithms into its most general framework, the theory of 1-motives. Written by leading experts in the field, it contains original results and finalises the theory of linear relations of 1-periods, answering long-standing questions in transcendence theory. It provides a complete exposition of the new theory for researchers, but also serves as an introduction to transcendence for graduate students and newcomers. It begins with foundational material, including a review of the theory of commutative algebraic groups and the analytic subgroup theorem as well as the basics of singular homology and de Rham cohomology. Part II addresses periods of 1-motives, linking back to classical examples like the transcendence of &#960;, before the authors turn to periods of algebraic varieties in Part III. Finally, Part IV aims at a dimension formula for the space of periods of a 1-motive in terms of its data.</p>

Transcendence and Linear Relations of 1-Periods (Cambridge Tracts in Mathematics)

Science & Math

Wüstholz, Gisbert

Huber, Annette

Mathematics

Cambridge University Press

This book consists of the notes from the seminar Bonn/ Wuppertal 1983/ 84 on Arithmetic Geometry. It contains a proof for the Mordell conjecture and may be useful as an introduction to Arakelov's point of view in diophantine geometry. The third edition includes an appendix in which a detailed survey on the spectacular recent developments in arithmetic algebraic geometry is given. These beautiful new results have their roots in the material covered by this book.

Rational Points: Seminar Bonn/Wuppertal 1983/84 (Aspects of Mathematics)

Faltings, Gerd

Vieweg+Teubner Verlag

<p>I: Moduli Spaces.- II: Heights.- III: Some Facts from the Theory of Group Schemes (Fritz Grunewald).- IV: Tate'S Conjecture on the Endomorphisms of Abelian Varieties (Norbert Schappacher).- V: The Finiteness Theorems of Faltings.- VI: Complements.- VII: Intersection Theory on Arithmetic Surfaces.</p>

Rational Points: Seminar Bonn/Wuppertal 1983/84 (Aspects of Mathematics, 2)

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