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        45 views

        Endomorphism rings of deformations of a height $h$ formal group law

        Let $k$ be an algebraically closed field of characterstic $p$, $H_0$ be a height $h$ formal group law over $k$. For any complete noetherian $W(k)$ algebra with residue field $k$, we can consider the ...
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        0answers
        72 views

        Geometric intuition and computation for Cartier theory

        I am learning Cartier theory of commutative formal groups by the book of Zink. It is a powerful tool but I don't understand it's motivation. The Cartier module of a formal group $G$ over a $\mathbb{Z}...
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        1k views

        Characterizing positivity of formal group laws

        The formal group law associated with a generating function $f(x) = x + \sum_{n=2}^\infty a_n \frac{x^n}{n!}$ is $$f(f^{-1}(x) + f^{-1}(y)).$$ In my thesis, I found a large number of examples of ...
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        85 views

        Formal Group Laws in a lined topos

        I am aware of the following: in the context of synthetic differential geometry (SDG) one obtains a Lie algebra by exponentiating a microlinear group by a standard infinitesimal object and taking the ...
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        votes
        1answer
        260 views

        What is the essential image of $AbVar$ in $p-div$?

        Given an abelian variety $A$ over a base scheme $\text{Spec } \mathcal{O}_{K_p}$, we define the functor $P$ as taking $A \mapsto \text{colim}_n A[p^n]$, its associated $p$-divisible group. What is the ...
        8
        votes
        1answer
        221 views

        (Pre)orientation vs. formal completion

        Let $\mathbb G$ be an abelian vatiety over an $\mathbb E_\infty$-ring $A$. That is to say, it consists of an abelian group object in the $\infty$-category of relative schemes $\mathbb G\to \...
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        3answers
        193 views

        Morphisms of formal group laws $\,F_a \rightarrow F_m\,$ and $\,F_m\to F_m$

        While studying cohomology theories on the stable homotopy setting, I have come up with the following basic question: Consider the additive formal group law, $F_a$, and the multiplicative formal group ...
        8
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        1answer
        435 views

        deformation theory in positive characteristic

        The idea "Formal deformation theory in characteristic zero is controlled by a differential graded Lie algebra (dgla)" goes back to Goldman-Millson, Deligne, Drinfeld among others; see Lurie's ICM talk....
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        204 views

        Rational cohomology of formal multiplicative group

        Let $\hat{\mathbb G}$ be a formal group over a field $k$, and let $V$ be a finite dimensional algebraic representation of $\hat{\mathbb G}$ (meaning we have fixed a homomorphism of algebraic groups $\...
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        341 views

        Geometry underlying a comparison of Dieudonné theories

        Maybe these hypotheses aren't necessary, but for me $\mathbb G$ will be a smooth formal group of dimension 1 and finite height over a perfect field $k$. There are several presentations of the ...
        10
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        2answers
        629 views

        How to compute the formal group law of a Shimura variety (using its invariant differentials)?

        I have a 3 dimensional abelian variety whose formal group law breaks into a formal summand where one of the pieces is one-dimensional. I am desperately wondering how to compute the $p$-series of ...
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        votes
        0answers
        171 views

        Definition of logarithm for universal vector extension

        Let $S$ be a topological $\mathbb{Z}_p$-algebra and $R\to S$ a surjection (where $R$ has $p$ nilpotent) with topologically nilpotent kernel which has a PD structure. We know that if $G/R$ is a $p$-...
        2
        votes
        0answers
        192 views

        Reduction “modulo $p$” of $\mathfrak{p}$-torsion points of CM elliptic curves

        Let $E/L$ be an elliptic curve defined over a number field $L$. Assume moreover that $E$ has complex multiplication by an imaginary quadratic field $K$. Let $\mathfrak{p}$ be a prime ideal of $K$. ...
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        0answers
        171 views

        “Algebrazing” canonical subgroups of elliptic curves

        I'm puzzled by a part of the construction of the canonical subgroup of a "not too supersingular" elliptic curve. In Katz's paper, one produces a subgroup of the formal group of the elliptic curve but ...
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        votes
        1answer
        122 views

        Functional equations associated with addition theorems for elliptic functions

        I'm trying to read the article "Functional equations associated with addition theorems for elliptic functions and two-valued algebraic groups" by Bukhshtaber,V. M. Russian Mathematical Surveys(1990),...

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