We apply a theorem of J. Lurie to produce cohomology theories associated to certain
Shimura varieties of type $ U (1, n-1) $. These cohomology theories of topological …

We study modular approximations Q (ℓ), ℓ= 3, 5, of the K (2)–local sphere at the prime 2 that
arise from ℓ–power degree isogenies of elliptic curves. We develop Hopf algebroid level …

The goal of this paper is to develop some of the machinery necessary for doing K (2)–local
computations in the stable homotopy category using duality resolutions at the prime p= 2 …

We analyze the ring tmf∗ tmf of cooperations for the connective spectrum of topological
modular forms (at the prime 2) through a variety of perspectives:(1) the E 2‐term of the …

We characterize the 2–line of the p–local Adams–Novikov spectral sequence in terms of
modular forms satisfying a certain explicit congruence condition for primes p≥ 5. We give a …

We investigate a dense subgroup Γ of the second Morava stabilizer group given by a certain
group of quasi-isogenies of a supersingular elliptic curve in characteristic p. The group Γ …

-3mu--family congruences and the f-5mu--invariant Page 1 Geometry & Topology Monographs
16 (2009) 9–29 9 ˇ–family congruences and the f–invariant MARK BEHRENS GERD LAURES …

We describe a vanishing result on the cohomology of a cochain complex associated to the
moduli of chains of finite subgroup schemes on elliptic curves. These results have …

Given a maximal finite subgroup G of the nth Morava stabilizer group at a prime p, we
address the question: is the associated higher real K‐theory EOn a summand of the K (n) …

For every prime p and integer n≥ 3 we explicitly construct an abelian variety of dimension n
such that for a suitable prime l the group of quasi-isogenies of of l-power degree is …