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ON THE MODULARITY OF ELLIPTIC CURVES OVER Q: WILD 3-ADIC EXERCISES.
Elliptic curve Galois representation modularity
2015/7/6
with c 0 mod N and d p mod N. The operators Tp for p6 jN can be simultaneously diagonalised on
the space Sk(N) and a simultaneous eigenvector is called an eigenform. If f is an eigenform then the...
MODULARITY OF CERTAIN POTENTIALLY BARSOTTI-TATE GALOIS REPRESENTATIONS
CERTAIN POTENTIALLY REPRESENTATIONS
2015/7/6
where is the reduction of . These results were subject to hypotheses on the local
behavior of at `, i.e., the restriction of to a decomposition group at `, and to
irreducibility hypotheses on...
ANOMALY CANCELLATION AND MODULARITY II: THE E8 × E8 CASE
ANOMALY CANCELLATION MODULARITY II THE E8 × E8 CASE
2018/4/19
In this paper we show that both of the Green-Schwarz anomaly factorization formulafor the gauge group E8 × E8 and the Hoˇrava-Witten anomaly factorization formula for the gaugegroup E8 can be derived ...
It has been shown that the Alvarez-Gaum′e-Witten miraculous anomaly cancellation formula in type IIB superstring theory and its various generalizations can be derived from modularity of certain charac...
Modularity lifting results in parallel weight one and applications to the Artin conjecture: the tamely ramified case
Modularity lifting results parallel weight one Artin conjecture tamely ramified case Number Theory
2012/4/18
We extend the modularity lifting result of the arXiv:1111.2804 to allow Galois representations with some ramification at p. We also prove modularity mod 2 and 5 of certain Galois representations. We u...
Identifying and understanding modular organizations is centrally important in the study of complex systems. Several approaches to this problem have been advanced, many framed in information-theoretic ...