Akhil Mathew

The Picard group of topological modular forms via descent theory

This paper starts with an exposition of descent-theoretic techniques in the study of Picard groups of

Nilpotence and descent in equivariant stable homotopy theory

\mathbf{E}_{\infty}

A thick subcategory theorem for modules over certain ring spectra

-ring spectra, which naturally lead to the study of Picard spectra. We then develop tools for the efficient and explicit determination of differentials in the associated descent spectral sequences for the Picard spectra thus obtained. As a major application, we calculate the Picard groups of the periodic spectrum of topological modular forms

Affineness and chromatic homotopy theory

TMF

On a nilpotence conjecture of J.P. May

and the non-periodic and non-connective

Picard groups of higher real K-theory spectra at height p - 1

Tmf

THH and base-change for Galois extensions of ring spectra

. We find that

Fibers of partial totalizations of a pointed cosimplicial space

\mathrm{Pic} (TMF)

Torsion exponents in stable homotopy and the Hurewicz homomorphism

is cyclic of order 576, generated by the suspension

The Galois group of a stable homotopy theory

\Sigma TMF