Isogenies of formal groups

Sporadic isogenies to orthogonal groups

SO(p, q) = {g ∈ SLp+q(R) : g>Qg = Q} (where Q = ( 1p 0 0 −1q ) )  SU(2) −→ SO(3) SL2(R) −→ SO(2, 1) SU(2)× SU(2) −→ SO(4) SL2(C) −→ SO(3, 1) SL2(R)× SL2(R) −→ SO(2, 2) Sp∗(2, 0) −→ SO(5) Sp∗(1, 1) −→ SO(4, 1) Sp2(R) −→ SO(3, 2) SU(4) −→ SO(6) SL2(H) −→ SO(5, 1) SU(2, 2) −→ SO(4, 2) SL4(R) −→ SO(3, 3) Thus, these are small examples...

Quasi-isogenies and Morava stabilizer groups

For every prime p and integer n > 3 we explicitly construct an abelian variety A/Fpn of dimension n such that for a suitable prime l the group of quasi-isogenies of A/Fpn of l-power degree is canonically a dense subgroup of the n-th Morava stabilizer group at p. We also give a variant of this result taking into account a polarization. This is motivated by the recent construction of topological ...

One-dimensional Formal Groups

In this Wednesday night section for Algebraic Number Theory, we will go through basic facts about one dimensional formal groups and hopefully get to see how they might be useful and interesting. All rings are commutative with identity. The sources of this material are my notes from Elliptic Curves, a course taught by Tom Fisher at Cambridge last year, J. Silverman’s Elliptic Curves Book. A few ...

Formal Deformation of Chow Groups

Especially notable here is Spencer Bloch’s semi-regularity paper [B]. The advantage of this approach is that one can use the full strength of the deformation theory of subvarieties. One might similarly ask whether there is a family of algebraic cycles {Zt}t∈B deforming Z; some first steps toward an infinitesimal theory for this problem were the subject of [G-G2]. A third possible context, which...

Bi-extensions of Formal Groups