منابع مشابه
Topological Automorphic Forms
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 automorphic forms (TAF ) are related to Shimura varieties in the same way that TMF is related to the moduli space of elliptic curves. We study the cohomology operations on these theories, and relate them to certain Hecke algebras. We c...
متن کاملTopological Automorphic Forms on U(1, 1)
The homotopy type and homotopy groups of some spectra TAFGU of topological automorphic forms associated to a unitary similitude group GU of type (1, 1) are explicitly described in quasi-split cases. The spectrum TAFGU is shown to be closely related to the spectrum TMF in these cases, and homotopy groups of some of these spectra are explicitly computed.
متن کاملThe 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.
متن کاملHigher real K-theories and topological automorphic forms
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)-localization of a TAF-spectrum associated to a unitary similitude group of type U(1, n − 1)? We answer this question in the affirmative for p ∈ {2, 3, 5, 7} and n = (p − 1)pr−1 for a maximal finite subgroup containing an ele...
متن کاملAutomorphic Forms
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 automorphic forms (TAF ) are related to Shimura varieties in the same way that TMF is related to the moduli space of elliptic curves. We study the cohomology operations on these theories, and relate them to certain Hecke algebras. We c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Memoirs of the American Mathematical Society
سال: 2010
ISSN: 0065-9266,1947-6221
DOI: 10.1090/s0065-9266-09-00573-0