A Family of Calabi–Yau Varieties and Potential Automorphy II

264 citations recorded by the source corpus.

Citations in the corpus

Even Galois representations and the Fontaine–Mazur conjecture (2009, unknown): “1 of [BLGHT09] without local-global compatibility, allowing for a modularity lifting theorem in the potentially semi-stable case.”
p-ADIC GEOMETRY (2017, unknown): “ll places. Theorem 5.3 is proved by establishing the potential automorphy of E and of all symmetric powers of Eresp. ˇ; here \potential" means after base change to (many) extensions F=F~ , as in [BLGHT11] where the case of totally real Fis proved. Thus, the second part follows Langlands’s strat”
Congruences between Hilbert modular forms: constructing ordinary lifts (2010, unknown): “We will also use the notion of a RAECSDC automorphic representation, for which see section 1 of [BLGHT09].”
Modularity lifting beyond the Taylor–Wiles method (2012, unknown): “4 of [76]) using the theorem of Moret–Bailly (in the form of Proposition 6.”
On torsion in the cohomology of locally symmetric varieties (2013, unknown): “1 might be within reach for regular L-algebraic cuspidal automorphic representations (corresponding to Galois representations with regular Hodge-Tate weights) over totally real or CM fields, at least in special cases or ‘potentially’ as in [10].”
On signs of Fourier coefficients of cusp forms (2011, unknown): “Now we are ready to state the second theorem.”
Local-global compatibility for $l=p$, II (2011, unknown): “where rl,ı(χ) : GF+ → Q × l is as defined in Section 1 of [BLGHT09].”