Paper XII: Patching Support, Hecke Packets, and Conditional Automorphic Completion

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1 @book{AtiyahMacdonald1969,
2   author = {Atiyah, Michael F. and Macdonald, Ian G.},
3   title = {Introduction to Commutative Algebra},
4   publisher = {Addison Wesley},
5   address = {Reading, Massachusetts},
6   year = {1969}
7 }
8 
9 @article{AllenEtAl2023,
10   author = {Allen, Patrick B. and Calegari, Frank and Caraiani, Ana and Gee, Toby and Helm, David and Le Hung, Bao V. and Newton, James and Scholze, Peter and Taylor, Richard and Thorne, Jack A.},
11   title = {Potential automorphy over {CM} fields},
12   journal = {Annals of Mathematics},
13   series = {2},
14   volume = {197},
15   number = {3},
16   year = {2023},
17   pages = {897{\textendash}1113}
18 }
19 
20 @book{BellaicheChenevier2009,
21   author = {Bella{\"i}che, Jo{\"e}l and Chenevier, Ga{\"e}tan},
22   title = {Families of {Galois} Representations and {Selmer} Groups},
23   series = {Ast{\'e}risque},
24   volume = {324},
25   publisher = {Soci{\'e}t{\'e} Math{\'e}matique de France},
26   address = {Paris},
27   year = {2009},
28   pages = {1{\textendash}314}
29 }
30 
31 @article{BrauerNesbitt1941,
32   author = {Brauer, Richard and Nesbitt, Cecil},
33   title = {On the modular characters of groups},
34   journal = {Annals of Mathematics},
35   volume = {42},
36   number = {2},
37   year = {1941},
38   pages = {556{\textendash}590}
39 }
40 
41 @article{CalegariGeraghty2018,
42   author = {Calegari, Frank and Geraghty, David},
43   title = {Modularity lifting beyond the {Taylor Wiles} method},
44   journal = {Inventiones Mathematicae},
45   volume = {211},
46   number = {1},
47   year = {2018},
48   pages = {297{\textendash}433}
49 }
50 
51 @article{CaraianiScholze2017,
52   author = {Caraiani, Ana and Scholze, Peter},
53   title = {On the generic part of the cohomology of compact unitary {Shimura} varieties},
54   journal = {Annals of Mathematics},
55   series = {2},
56   volume = {186},
57   number = {3},
58   year = {2017},
59   pages = {649{\textendash}766}
60 }
61 
62 @article{ClozelHarrisTaylor2008,
63   author = {Clozel, Laurent and Harris, Michael and Taylor, Richard},
64   title = {Automorphy for some {$l$} adic lifts of automorphic mod {$l$} {Galois} representations},
65   journal = {Publications Math{\'e}matiques de l'IH{\'E}S},
66   volume = {108},
67   year = {2008},
68   pages = {1{\textendash}181}
69 }
70 
71 @article{Diamond1997,
72   author = {Diamond, Fred},
73   title = {The {Taylor Wiles} construction and multiplicity one},
74   journal = {Inventiones Mathematicae},
75   volume = {128},
76   number = {2},
77   year = {1997},
78   pages = {379{\textendash}391}
79 }
80 
81 @book{Diestel2017,
82   author = {Diestel, Reinhard},
83   title = {Graph Theory},
84   edition = {Fifth},
85   series = {Graduate Texts in Mathematics},
86   volume = {173},
87   publisher = {Springer},
88   address = {Berlin},
89   year = {2017}
90 }
91 
92 @book{Eisenbud1995,
93   author = {Eisenbud, David},
94   title = {Commutative Algebra with a View Toward Algebraic Geometry},
95   series = {Graduate Texts in Mathematics},
96   volume = {150},
97   publisher = {Springer},
98   address = {New York},
99   year = {1995}
100 }
101 
102 @article{Gee2022,
103   author = {Gee, Toby},
104   title = {Modularity lifting theorems},
105   journal = {Essential Number Theory},
106   volume = {1},
107   number = {1},
108   year = {2022},
109   pages = {73{\textendash}126}
110 }
111 
112 @article{GuralnickHerzigTaylorThorne2012,
113   author = {Guralnick, Robert and Herzig, Florian and Taylor, Richard and Thorne, Jack A.},
114   title = {Adequate subgroups},
115   journal = {Journal of the Institute of Mathematics of Jussieu},
116   volume = {11},
117   number = {4},
118   year = {2012},
119   pages = {907{\textendash}920},
120   note = {Appendix to Jack A. Thorne, On the automorphy of l-adic Galois representations with small residual image}
121 }
122 
123 @article{Kisin2009,
124   author = {Kisin, Mark},
125   title = {Moduli of finite flat group schemes, and modularity},
126   journal = {Annals of Mathematics},
127   series = {2},
128   volume = {170},
129   number = {3},
130   year = {2009},
131   pages = {1085{\textendash}1180}
132 }
133 
134 @book{Matsumura1989,
135   author = {Matsumura, Hideyuki},
136   title = {Commutative Ring Theory},
137   edition = {Second},
138   series = {Cambridge Studies in Advanced Mathematics},
139   volume = {8},
140   publisher = {Cambridge University Press},
141   address = {Cambridge},
142   year = {1989}
143 }
144 
145 @incollection{Mazur1989,
146   author = {Mazur, Barry},
147   title = {Deforming {Galois} representations},
148   booktitle = {Galois Groups over {$\mathbb Q$}},
149   editor = {Ihara, Yasutaka and Ribet, Kenneth and Serre, Jean Pierre},
150   series = {Mathematical Sciences Research Institute Publications},
151   volume = {16},
152   publisher = {Springer},
153   address = {New York},
154   year = {1989},
155   pages = {385{\textendash}437}
156 }
157 
158 @article{MiagkovThorne2023,
159   author = {Miagkov, Konstantin and Thorne, Jack A.},
160   title = {Automorphy lifting with adequate image},
161   journal = {Forum of Mathematics, Sigma},
162   volume = {11},
163   year = {2023},
164   pages = {e8, 31 pages}
165 }
166 
167 @book{Neukirch1999,
168   author = {Neukirch, J{\"u}rgen},
169   title = {Algebraic Number Theory},
170   series = {Grundlehren der Mathematischen Wissenschaften},
171   volume = {322},
172   publisher = {Springer},
173   address = {Berlin},
174   year = {1999}
175 }
176 
177 @article{NewtonThorne2016,
178   author = {Newton, James and Thorne, Jack A.},
179   title = {Torsion {Galois} representations over {CM} fields and {Hecke} algebras in the derived category},
180   journal = {Forum of Mathematics, Sigma},
181   volume = {4},
182   year = {2016},
183   pages = {e21, 88 pages}
184 }
185 
186 @book{RibesZalesskii2010,
187   author = {Ribes, Luis and Zalesskii, Pavel},
188   title = {Profinite Groups},
189   edition = {Second},
190   series = {Ergebnisse der Mathematik und ihrer Grenzgebiete},
191   volume = {40},
192   publisher = {Springer},
193   address = {Berlin},
194   year = {2010}
195 }
196 
197 @article{Schlessinger1968,
198   author = {Schlessinger, Michael},
199   title = {Functors of {Artin} rings},
200   journal = {Transactions of the American Mathematical Society},
201   volume = {130},
202   number = {2},
203   year = {1968},
204   pages = {208{\textendash}222}
205 }
206 
207 @article{Scholze2015,
208   author = {Scholze, Peter},
209   title = {On torsion in the cohomology of locally symmetric varieties},
210   journal = {Annals of Mathematics},
211   series = {2},
212   volume = {182},
213   number = {3},
214   year = {2015},
215   pages = {945{\textendash}1066}
216 }
217 
218 @book{Serre1977,
219   author = {Serre, Jean Pierre},
220   title = {Linear Representations of Finite Groups},
221   series = {Graduate Texts in Mathematics},
222   volume = {42},
223   publisher = {Springer},
224   address = {New York},
225   year = {1977}
226 }
227 
228 @article{TaylorWiles1995,
229   author = {Taylor, Richard and Wiles, Andrew},
230   title = {Ring theoretic properties of certain {Hecke} algebras},
231   journal = {Annals of Mathematics},
232   series = {2},
233   volume = {141},
234   number = {3},
235   year = {1995},
236   pages = {553{\textendash}572}
237 }
238 
239 @article{Thorne2012,
240   author = {Thorne, Jack A.},
241   title = {On the automorphy of {$l$} adic {Galois} representations with small residual image},
242   journal = {Journal of the Institute of Mathematics of Jussieu},
243   volume = {11},
244   number = {4},
245   year = {2012},
246   pages = {855{\textendash}920}
247 }
248 
249 @article{Wiles1995,
250   author = {Wiles, Andrew},
251   title = {Modular elliptic curves and {Fermat}'s last theorem},
252   journal = {Annals of Mathematics},
253   series = {2},
254   volume = {141},
255   number = {3},
256   year = {1995},
257   pages = {443{\textendash}551}
258 }
259 
260 @book{Weibel1994,
261   author = {Weibel, Charles A.},
262   title = {An Introduction to Homological Algebra},
263   series = {Cambridge Studies in Advanced Mathematics},
264   volume = {38},
265   publisher = {Cambridge University Press},
266   address = {Cambridge},
267   year = {1994}
268 }
269 
270 @article{BarnetLambGeeGeraghtyTaylor2014,
271   author = {Barnet Lamb, Thomas and Gee, Toby and Geraghty, David and Taylor, Richard},
272   title = {Potential automorphy and change of weight},
273   journal = {Annals of Mathematics},
274   series = {2},
275   volume = {179},
276   number = {2},
277   year = {2014},
278   pages = {501{\textendash}609}
279 }

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