Among topological modular forms with level structure,\, TMF\, _0 (7) TMF 0 (7) at the prime 3
is the first example that had not been understood yet. We provide a splitting of\, TMF\, _0 (7) …

Topological modular forms with level structure were introduced in full generality by Hill and
Lawson. We will show that these decompose additively in many cases into a few simple …

We show that at the prime 2, for any height $ h $ and $ G\subset\mathbb {G} _h $ a finite
subgroup of the Morava stabilizer group, the $ RO (G) $-graded homotopy fixed point …

Connective models for topological modular forms of level n Page 1 T Algebraic & Geometric
Topology msp Volume 23 (2023) Connective models for topological modular forms of level n …

∗ E-comodules. Using this, we develop a theory of (relative) homological algebra for Morava
modules. We use this to give an explicit identification of the E2-term of the K (n)-local En …

We explore the C2-equivariant spectra T mf1 (3) and TMF1 (3). In particular, we compute
their C2-equivariant Picard groups and the C2-equivariant Anderson dual of T mf1 (3). This …

Let $ A\to B $ be a $ G $-Galois extension of rings, or more generally of $\mathbb {E} _\infty
$-ring spectra in the sense of Rognes. A basic question in algebraic $ K $-theory asks how …

John Rognes developed a notion of Galois extension of commutative ring spectra, and this
includes a criterion for identifying an extension as unramified. Ramification for commutative …

The synthetic analogue functor $\nu $ from spectra to synthetic spectra does not preserve all
limits. In this paper, we give a necessary and sufficient criterion for $\nu $ to preserve the …

We begin by investigating analogues of the Ravenel conjectures in chromatic homotopy in
the setting of Real-oriented homotopy theory, where one carries the data of canonical group …