750 research outputs found
The Shimura curve of discriminant 15 and topological automorphic forms
We find defining equations for the Shimura curve of discriminant 15 over
Z[1/15]. We then determine the graded ring of automorphic forms over the 2-adic
integers, as well as the higher cohomology. We apply this to calculate the
homotopy groups of a spectrum of "topological automorphic forms" associated to
this curve, as well as one associated to a quotient by an Atkin-Lehner
involution.Comment: 36 pages, 5 figures, updated with corrections and new introduction
(this version corrects image issues in the previous
Structured ring spectra and displays
We combine Lurie's generalization of the Hopkins-Miller theorem with work of
Zink-Lau on displays to give a functorial construction of even-periodic
commutative ring spectra, concentrated in chromatic layers 2 and above,
associated to certain n by n invertible matrices with coefficients in Witt
rings. This is applied to examples related to Lubin-Tate and Johnson-Wilson
spectra. We also give a Hopf algebroid presentation of the moduli of
p-divisible groups of height greater than or equal to 2.Comment: 18 page
The Bott cofiber sequence in deformation K-theory and simultaneous similarity in U(n)
We show that there is a homotopy cofiber sequence of spectra relating
Carlsson's deformation K-theory of a group G to its "deformation representation
ring," analogous to the Bott periodicity sequence relating connective K-theory
to ordinary homology. We then apply this to study simultaneous similarity of
unitary matrices
Regularity of structured ring spectra and localization in K-theory
We identify a regularity property for structured ring spectra, and with it we
prove a natural analogue of Quillen's localization theorem for algebraic
K-theory in this setting.Comment: 9 pages. Corrected references and aspects of the expositio
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