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Prime-Contact Coherence Calculus

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1 \chapter{Bibliographic Orientation}
2 
3 The internal reductions and finite algebra in this paper are proved in the text. The references below identify the established theories used for context, terminology, or external input.
4 
5 \begin{thebibliography}{99}
6 
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8 H. Pasten,
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10 arXiv:2106.16165, 2021.
11 
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13 P. Vojta,
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17 
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22 The present paper does not use these papers as an established proof of $abc$.
23 
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26 ``Why $abc$ is still a conjecture,''
27 manuscript, 2018.
28 
29 \bibitem{Wiles}
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33 \href{https://doi.org/10.2307/2118559}{doi:10.2307/2118559}.
34 
35 \bibitem{TaylorWiles}
36 R. Taylor and A. Wiles,
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38 \emph{Annals of Mathematics} 141 (1995), 553--572.
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40 
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44 \emph{Journal of the American Mathematical Society} 14 (2001), 843--939.
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46 
47 \bibitem{Agashe}
48 A. Agashe,
49 ``The modular number, congruence number, and multiplicity one,''
50 arXiv:0810.5176, 2008.
51 
52 \bibitem{CesnaviciusManin}
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54 ``The Manin constant and the modular degree,''
55 arXiv:1911.09446, 2019.
56 
57 \bibitem{PastenShimura}
58 H. Pasten,
59 ``Shimura curves and the $abc$ conjecture,''
60 arXiv:1705.09251, 2017.
61 
62 \bibitem{BKM1}
63 G. B\"ockle, C. Khare, and J. Manning,
64 ``Wiles defect for Hecke algebras that are not complete intersections,''
65 \emph{Compositio Mathematica} 157 (2021), 1908--1954.
66 arXiv:1910.08507.
67 
68 \bibitem{BKM2}
69 G. B\"ockle, C. Khare, and J. Manning,
70 ``Wiles defect of Hecke algebras via local-global arguments,''
71 \emph{Journal of the Institute of Mathematics of Jussieu} 22 (2023), 2601--2649.
72 arXiv:2108.09729.
73 
74 \bibitem{SerreLocalFields}
75 J.-P. Serre,
76 \emph{Local Fields},
77 Graduate Texts in Mathematics 67, Springer, 1979.
78 
79 \bibitem{DGM}
80 B. Dundas, T. Goodwillie, and R. McCarthy,
81 \emph{The Local Structure of Algebraic K-Theory},
82 Springer, 2013.
83 
84 \bibitem{AKN}
85 B. Antieau, A. Krause, and T. Nikolaus,
86 ``On the K-theory of $\mathbb Z/p^n$,''
87 arXiv:2405.04329, 2024.
88 
89 \bibitem{AokiFermat}
90 N. Aoki,
91 ``Simple factors of the Jacobian of a Fermat curve and the Picard number of a product of Fermat curves,''
92 \emph{American Journal of Mathematics} 113 (1991), 779--833.
93 \href{https://doi.org/10.2307/2374786}{doi:10.2307/2374786}.
94 
95 \bibitem{ColemanMcCallum}
96 R. Coleman and W. McCallum,
97 ``Stable reduction of Fermat curves and Jacobi sum Hecke characters,''
98 \emph{Journal f\"ur die reine und angewandte Mathematik} 385 (1988), 41--101.
99 \href{https://doi.org/10.1515/crll.1988.385.41}{doi:10.1515/crll.1988.385.41}.
100 
101 \bibitem{OtsuboYamazaki}
102 N. Otsubo and T. Yamazaki,
103 ``Motivic Gauss and Jacobi sums,''
104 arXiv:2402.06072, 2024.
105 
106 \bibitem{Goncharov}
107 A. B. Goncharov,
108 ``Multiple polylogarithms and mixed Tate motives,''
109 arXiv:math/0103059, 2001.
110 
111 \bibitem{ZagierPolylog}
112 D. Zagier,
113 ``Polylogarithms, Dedekind zeta functions, and the algebraic K-theory of fields,''
114 in \emph{Arithmetic Algebraic Geometry}, Progress in Mathematics 89,
115 Birkh\"auser, 1991, 391--430.
116 \href{https://doi.org/10.1007/978-1-4612-0457-2_19}{doi:10.1007/978-1-4612-0457-2\_19}.
117 
118 \bibitem{Borel}
119 A. Borel,
120 ``Stable real cohomology of arithmetic groups,''
121 \emph{Annales scientifiques de l'\'Ecole Normale Sup\'erieure} 7 (1974), 235--272.
122 \href{https://doi.org/10.24033/asens.1269}{doi:10.24033/asens.1269}.
123 
124 \bibitem{LLL}
125 A. K. Lenstra, H. W. Lenstra Jr., and L. Lov\'asz,
126 ``Factoring polynomials with rational coefficients,''
127 \emph{Mathematische Annalen} 261 (1982), 515--534.
128 \href{https://doi.org/10.1007/BF01457454}{doi:10.1007/BF01457454}.
129 
130 \bibitem{CVP}
131 D. Micciancio and P. Voulgaris,
132 ``A deterministic single exponential time algorithm for most lattice problems based on Voronoi cell computations,''
133 \emph{SIAM Journal on Computing} 42 (2013), 1364--1391.
134 \href{https://doi.org/10.1137/100811970}{doi:10.1137/100811970}.
135 
136 \bibitem{FRI}
137 M. Vetterli, P. Marziliano, and T. Blu,
138 ``Sampling signals with finite rate of innovation,''
139 \emph{IEEE Transactions on Signal Processing} 50 (2002), 1417--1428.
140 \href{https://doi.org/10.1109/TSP.2002.1003065}{doi:10.1109/TSP.2002.1003065}.
141 
142 \bibitem{GibbsReview}
143 D. Gottlieb and C.-W. Shu,
144 ``On the Gibbs phenomenon and its resolution,''
145 \emph{SIAM Review} 39 (1997), 644--668.
146 \href{https://doi.org/10.1137/S0036144596301390}{doi:10.1137/S0036144596301390}.
147 
148 \end{thebibliography}

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