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Algebraic classes in mixed characteristic and Andr\'e's p-adic periods
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abstract
Motivated by the study of algebraic classes in mixed characteristic we define a countable subalgebra of $\bar{\mathbb{Q}}_p$ which we call the algebra of Andr\'e's $p$-adic periods. We construct a tannakian framework to study these periods. In particular, we bound their transcendence degree and formulate the analog of the Grothendieck period conjecture. We exhibit several examples where special values of classical $p$-adic functions appear as Andr\'e's $p$-adic periods and we relate these new conjectures to some classical problems on algebraic classes.
Forward citations
Cited by 2 Pith papers
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P-adic Period Conjectures for 1-motives: Integration and Linear Relations
The authors construct p-adic integration pairings and Q-structures for 1-motives with good reduction, and claim that all linear relations among the resulting p-adic periods at depths 1 and 2 are captured by bilinearit...
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G-functions, motives, and unlikely intersections -- old and new
A survey of the G-function method, its link to periods, and its use in proving cases of unlikely intersection conjectures.
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