p-adic period map for the moduli space of deformations of a formal group

Demchenko, Oleg; Gurevich, Alexander

doi:10.1016/j.jalgebra.2004.12.017

Cited by 4 publications

(14 citation statements)

References 5 publications

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“…Thus there is more than one basis given by a d -tuple, as required. Let Φ (1) = F V (Ξ (1) ) and Φ (2) = F V (Ξ (2) ) be p-typical formal groups. Denote by Ξ (i) ∈ M d (O) ∞ , the sequences of matrices composed of the Teichmüller representatives of the entries of the corresponding matrices in the sequence…”

Section: Basis Of the Cokernel Of Y ξmentioning

confidence: 99%

“…(2) n n , respectively. If Φ (1) and Φ (2) are isomorphic then by Proposition A2 there exist invertible w, z ∈ M d (E) such that u (2) w = zu (1) . Suppose, in addition, that there exists a unique Ψ (2) specifying a basis of Coker Y Ξ (2) .…”

Section: Basis Of the Cokernel Of Y ξmentioning

confidence: 99%

“…If Φ (1) and Φ (2) are isomorphic then by Proposition A2 there exist invertible w, z ∈ M d (E) such that u (2) w = zu (1) . Suppose, in addition, that there exists a unique Ψ (2) specifying a basis of Coker Y Ξ (2) . Then Ψ (2) and w allow one to determine all possible choices of Ψ (1) specifying a basis of Coker Y Ξ (1) .…”

Section: Basis Of the Cokernel Of Y ξmentioning

confidence: 99%

“…Suppose, in addition, that there exists a unique Ψ (2) specifying a basis of Coker Y Ξ (2) . Then Ψ (2) and w allow one to determine all possible choices of Ψ (1) specifying a basis of Coker Y Ξ (1) . Indeed, U (2) W = ZU (1) , where…”

Section: Basis Of the Cokernel Of Y ξmentioning

confidence: 99%

“…In the case where dim G = 1, such a description was established in [2] with the aid of the universal deformation constructed by Hazewinkel. The universal deformation introduced in the present paper will hopefully allow us to treat similarly the action in the multidimensional case.…”

Section: Introductionmentioning

confidence: 99%

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On the moduli space of deformations of a $p$-divisible group

Demchenko

Gurevich

2014

Mathematical Research Letters

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Section: Basis Of the Cokernel Of Y ξmentioning

confidence: 99%

Section: Basis Of the Cokernel Of Y ξmentioning

confidence: 99%

Section: Basis Of the Cokernel Of Y ξmentioning

confidence: 99%

Section: Basis Of the Cokernel Of Y ξmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the moduli space of deformations of a $p$-divisible group

Demchenko

Gurevich

2014

Mathematical Research Letters

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Group Action on the Deformations of a Formal Group Over the Ring of Witt Vectors

Demchenko¹,

Gurevich²

2017

Nagoya Math. J.

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A recent result by the authors gives an explicit construction for a universal deformation of a formal group $\unicode[STIX]{x1D6F7}$ of finite height over a finite field $k$ . This provides in particular a parametrization of the set of deformations of $\unicode[STIX]{x1D6F7}$ over the ring ${\mathcal{O}}$ of Witt vectors over $k$ . Another parametrization of the same set can be obtained through the Dieudonné theory. We find an explicit relation between these parameterizations. As a consequence, we obtain an explicit expression for the action of $\text{Aut}_{k}(\unicode[STIX]{x1D6F7})$ on the set of ${\mathcal{O}}$ -deformations of $\unicode[STIX]{x1D6F7}$ in the coordinate system defined by the universal deformation. This generalizes a formula of Gross and Hopkins and the authors’ result for one-dimensional formal groups.

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Covariant Honda theory

Demchenko¹

2005

Tohoku Math. J. (2)

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Honda's theory gives an explicit description up to strict isomorphism of formal groups over perfect fields of characteristic p = 0 and over their rings of Witt vectors by means of attaching a certain matrix, which is called its type, to every formal group. A dual notion of right type connected with the reduction of the formal group is introduced while Honda's original type becomes a left type. An analogue of the Dieudonné module is constructed and an equivalence between the categories of formal groups and right modules satisfying certain conditions, similar to the classical anti-equivalence between the categories of formal groups, and left modules satisfying certain conditions is established. As an application, the -isomorphism classes of the deformations of a formal group over and the action of its automorphism group on these classes are studied.

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p-adic period map for the moduli space of deformations of a formal group

Cited by 4 publications

References 5 publications

On the moduli space of deformations of a $p$-divisible group

On the moduli space of deformations of a $p$-divisible group

Group Action on the Deformations of a Formal Group Over the Ring of Witt Vectors

Covariant Honda theory

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