Formal Group Laws Arising from Algebraic Varieties

Stienstra, Jan

doi:10.2307/2374494

Cited by 35 publications

(41 citation statements)

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“…We determine the formal group associated to H n−1 (V t , W O) of V t explicitly by writing down a formal group law G t for it (Proposition 5.2). For this, we will follow the work of Stienstra [12]. From this point of view, the series F appears as a certain p-adic limit of the coefficients of the logarithm of G t .…”

Section: The Dwork Familymentioning

confidence: 99%

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Variation of the unit root along the Dwork family of Calabi–Yau varieties

2008

Math. Ann.

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Section: The Dwork Familymentioning

confidence: 99%

“…By the description of the Newton polygon in the last paragraph, G t is of height 1, 2 or ∞. Notice that the formal group G t can be defined over a more general base ring A (see [12], Theorem 1).…”

Section: Theorem 22mentioning

confidence: 99%

Variation of the unit root along the Dwork family of Calabi–Yau varieties

2008

Math. Ann.

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“…In addition to their elegance (most notably in [18]), formal groups continue to find powerful and sometimes surprising applications in number theory, algebraic geometry and topology (see [3,20,21], for example).…”

Section: Introductionmentioning

confidence: 99%

On lifting commutative dynamical systems

Sarkis

2005

Journal of Algebra

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We construct a lifting of commuting power series from a residue field of positive characteristic to a local ring, in a manner similar to the formal group cohomologies of Lubin-Tate. This lifting is then used to prove that a nontorsion Z p automorphism and a multiplication-by-p endomorphism uniquely define a formal group over fields of a positive characteristic. This suggests that a characteristic 0 conjecture by Lubin could be approached with residue field considerations.

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“…The method applies to families of K3 surfaces satisfying certain conditions imposed in his Theorem [20,Theorem 2].…”

Section: An Applicationmentioning

confidence: 99%

“…The coefficients of logarithm l( ) of this formal group can be determined explicitly by the formula given in [20,Theorem 2]. In this case we get that…”

Section: An Applicationmentioning

confidence: 99%