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- W2963837469 abstract "We give a criterion of integrality of a one-dimensional formal group law in terms of congruences satisfied by the coefficients of the canonical invariant differential. For an integral formal group law a <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=p> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=application/x-tex>p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic analytic formula for the local characteristic polynomial at <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=p> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=application/x-tex>p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is given. We demonstrate applications of our results to formal group laws attached to <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding=application/x-tex>L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-functions, Artin–Mazur formal groups of algebraic varieties and hypergeometric formal group laws. This paper was written with the intention to give an explicit and self-contained introduction to the arithmetic of formal group laws, which would be suitable for non-experts. For this reason we consider only one-dimensional laws, though a generalization of our approach to higher dimensions is clearly possible. The ideas of congruences and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=p> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=application/x-tex>p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic continuity in the context of formal groups were considered by many authors. We sketch the relation of our results to the existing literature in a separate paragraph at the end of the introductory section." @default.
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- W2963837469 date "2018-07-12" @default.
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- W2963837469 title "Formal groups and congruences" @default.
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- W2963837469 doi "https://doi.org/10.1090/tran/7283" @default.
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