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Majumdar, Dipramit
- Endoscopic Transfer Between Eigenvarieties for Definite Unitary Groups
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1 Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pashan, Pune-411008, IN
1 Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pashan, Pune-411008, IN
Source
Journal of the Ramanujan Mathematical Society, Vol 31, No 3 (2016), Pagination: 235-255Abstract
In this paper, we extend the endoscopic transfer of definite unitary group U(n), which sends a pair of automorphic forms of U(n1),U(n2) to an automorphic form of U(n1+n2), to finite slope p-adic automorphic forms for definite unitary groups by constructing a rigid analytic map between eigenvarieties εn1×εn2→ε(n1+n2), which at classical points interpolates endoscopic transfer map.
- l-Class Groups of Cyclic Extensions of Prime Degree l
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Authors
Affiliations
1 Department of Mathematics, International Institute of Information Technology, 26/C, Electronics City, Hosur Road, Bangalore-560100, IN
2 Indian Institute of Science Education and Research, Dr. Homi Bhaba Road, Pashan, Pune-411008, IN
3 Stat-Math Unit, Indian Statistical Institute, 8th Mile Mysore Road, Bangalore-560059, IN
1 Department of Mathematics, International Institute of Information Technology, 26/C, Electronics City, Hosur Road, Bangalore-560100, IN
2 Indian Institute of Science Education and Research, Dr. Homi Bhaba Road, Pashan, Pune-411008, IN
3 Stat-Math Unit, Indian Statistical Institute, 8th Mile Mysore Road, Bangalore-560059, IN
Source
Journal of the Ramanujan Mathematical Society, Vol 30, No 4 (2015), Pagination: 413-454Abstract
Let K/F be a cyclic extension of odd prime degree l over a number field F. If F has class number coprime to l, we study the structure of the l-Sylow subgroup of the class group of K. In particular, when F contains the l-th ischolar_mains of unity, we obtain bounds for the 𝔽l-rank of the l-Sylow subgroup of K using genus theory. We obtain some results valid for general l. Following that, we obtain more complete, explicit results for l=5 and F=Q(e2iπ/5). The rank of the 5-class group of K is expressed in terms of power residue symbols. We compare our results with tables obtained using SAGE (the latter is under GRH).We obtain explicit results in several cases. These results have a number of potential applications. For instance, some of them like Theorem 5.16 could be useful in the arithmetic of elliptic curves over towers of the form Q(e2iπ/5n, x1/5). Using the results on the class groups of the fields of the form Q(e2iπ/5, x1/5), and using Kummer duality theory, we deduce results on the 5-class numbers of fields of the form Q(x1/5).- p-Adic Asai Transfer
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Authors
Affiliations
1 Department of Mathematics, Indian Institute of Science Education and Research Pune, Dr. Homi Bhabha Road, Pashan, Pune 411 008, IN
2 Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, IN
1 Department of Mathematics, Indian Institute of Science Education and Research Pune, Dr. Homi Bhabha Road, Pashan, Pune 411 008, IN
2 Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, IN
Source
Journal of the Ramanujan Mathematical Society, Vol 34, No 3 (2019), Pagination: 305-324Abstract
Let K/ℚ be a real quadratic field. Given an automorphic representation π for GL2/K, let As±(π) denote the plus/minus Asai transfer of π to an automorphic representation for GL4/ℚ. In this paper, we construct a rigid analytic map from a subvariety of the universal eigenvariety of GL2/K to an eigenvariety of GL4/ℚ, which at nice classical points interpolate this Asai transfer.References
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