Dr Jayanta Manoharmayum
School of Mathematical and Physical Sciences
Lecturer
+44 114 222 3871
Full contact details
School of Mathematical and Physical Sciences
J22
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
- Research interests
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The absolute Galois group of the rationals is my primary interest. It contains almost all arithmetic information: eg, solutions to explicit diophantine equations (as in Fermat's Last Theorem). The whole group in general is rather too large an object to study; a better way of understanding the Galois group is through its representations, and this brings out deep connections with other mathematical objects (such as modular forms). For example, given a two dimensional representation of the Galois group satisfying `usual conditions', there should be a modular form whose Fourier coefficients are related to the traces of the representation. The precise correspondences are conjecturally given by the conjectures of Artin (complex representations), Fontaine and Mazur (p-adic representations), and Serre (finite characteristic). It is aspects of these conjectures, both over the rationals and in the setting of totally real number fields, that I am most interested in.
- Publications
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Show: Featured publications All publications
Featured publications
Journal articles
- Lifting N-dimensional Galois representations to characteristic zero. Glasgow Mathematical Journal, 61(1), 115-150. View this article in WRRO
- The inverse deformation problem. Compositio Mathematica, 152(8), 1725-1739. View this article in WRRO
- A structure theorem for subgroups of GL_n over complete local Noetherian rings with large residual image. Proceedings of the American Mathematical Society, 143, 2743-2758. View this article in WRRO
All publications
Journal articles
- A note on the structure of complete alternative local algebras. Communications in Algebra. View this article in WRRO
- Lifting N-dimensional Galois representations to characteristic zero. Glasgow Mathematical Journal, 61(1), 115-150. View this article in WRRO
- The inverse deformation problem. Compositio Mathematica, 152(8), 1725-1739. View this article in WRRO
- A structure theorem for subgroups of GL_n over complete local Noetherian rings with large residual image. Proceedings of the American Mathematical Society, 143, 2743-2758. View this article in WRRO
- Higher congruence companion forms. Acta Arithmetica, 156, 159-175.
- Lifting Galois representations of number fields. J NUMBER THEORY, 129(5), 1178-1190.
- On the modularity of supersingular elliptic curves over certain totally real number fields. J NUMBER THEORY, 128(3), 589-618.
- A note on Serre's conjecture modulo 6. B LOND MATH SOC, 36, 216-220.
- Modularity of rigid Calabi-Yau threefolds over Q. Fields Institute Communications, 38. View this article in WRRO
- On the modularity of certain GL(2)(F7) Galois representations. MATH RES LETT, 8(5-6), 703-712.
- Abelian surfaces with level √5 structure. The Asian Journal of Mathematics, 3(3), 677-688.
- Pairs of mod 3 and mod 5 representations arising from elliptic curves. MATH RES LETT, 6(5-6), 735-754.
Conference proceedings papers
- Serre's conjecture for mod 7 Galois representations. MODULAR CURVES AND ABELIAN VARIETIES, Vol. 224 (pp 141-149)
Preprints
- The Artin--Rees lemma and size of spaces over nonassociative complete
filtered rings.
- Lifting N-dimensional Galois representations to characteristic zero. Glasgow Mathematical Journal, 61(1), 115-150. View this article in WRRO
- Research group
- Grants
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Past grants, as Principal Investigator
Modularity and Galois Respresentation of Totally Real Fields - Nuffield
- Teaching activities
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MAS110 Mathematics Core I