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Transcendence and Linear Relations of 1-Periods (Hardcover)
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Transcendence and Linear Relations of 1-Periods (Hardcover)
Series: Cambridge Tracts in Mathematics
Expected to ship within 12 - 19 working days
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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 , 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.
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