- role in
modern number theory. In mathematics, the
notion of
factor of
automorphy arises for a
group acting on a complex-analytic manifold.
Suppose a group...
- {\displaystyle j} is the identity. Some
facts about factors of
automorphy:
Every factor of
automorphy is a
cocycle for the
action of G {\displaystyle G} on the...
-
functions with
factor of
automorphy a ( H , χ ) {\displaystyle a_{(H,\chi )}} . Sometimes, this is
called the
canonical factor of
automorphy for L {\displaystyle...
- GL(n) over CM fields. Thorne's 2015
joint work with
Khare on
potential automorphy and Leopoldt's
conjecture has led to a
proof of a
potential version of...
-
class of any
factor of
automorphy is a
Riemann form. Conversely,
given any
Riemann form, we can
construct a
factor of
automorphy such that the alternatization...
-
applies where the j-invariant is not integral. Taylor,
Richard (2008). "
Automorphy for some l-adic
lifts of
automorphic mod l
Galois representations. II"...
-
University Press, ISBN 978-0-691-09092-4, MR 1876802 Taylor,
Richard (2008). "
Automorphy for some l-adic
lifts of
automorphic mod l
Galois representations. II"...
-
particular for the proof, in
collaboration with
James Newton, of the
automorphy of all
symmetric powers of a
holomorphic modular newform."
Jacob Tsimerman...
- (4): 843–939. doi:10.1090/S0894-0347-01-00370-8. Taylor, R. (2008). "
Automorphy for some l-adic
lifts of
automorphic mod l representations. II". Publications...
- ; Taylor, R. (2010). "A
family of Calabi–Yau
varieties and
potential automorphy".
Annals of Mathematics. 171 (2): 779–813. doi:10.4007/annals.2010.171...
