E-mail : firstname.lastname@example.org
Fax (department) : (518) 442-4731
University of Illinois at Urbana-Champaign (Advisors : I. Reiner,
S. V. Ullom).
My area of reseach is in algebraic number theory. I am particularly interested in Galois module theory. There is a nice introduction to some problems in Galois module theory at L. N. Childs' home page. My interest is motivated by relationships between algebro-arithmetic invariants and analytic invariants associated with Galois
extension of number fields. If M/K is a Galois extension of number fields with
Galois group G, an algebro-arithmetic invariant is associated to the H-module S in a classgroup of H, where S is the ring of integers of M and H is the associated order of S in the group algebra KG. Analytic invariants arise from L-functions (or p-adic L-functions) associated with number fields K and M.
Much of my work has been about such algebro-arithmetic invariants that come from a subgroup of the classgroup of H, called the Swan subgroup. I am also interested in the theory of cyclotomic fields and the arithmetic of elliptic curves.
Millennial Conference on Number Theory , University of Illinois at Urbana-Champaign, May 2000.
International Conference on Discrete Mathematics and Number Theory , Tiruchirapalli, India, January 1996.
Workshop on Galois Module Structures, The Fields Institute, Canada, February 1994.
"Swan modules and elliptic functions", Illinois J. Math. , vol. 32 (3),
" A note on Swan modules", Indian J. Pure Appl. Math. , vol. 20 (11), 1989, 1067-1076.
"Elliptic Curves with Complex Multiplication and Galois module structure"
(with M.J. Taylor ), Invent, Math. , vol. 99, 1990, 165-184.
"Modules de Swan et courbes elliptiques a multiplication complexe",
Seminaire de la Theorie des Nombres, Bordeaux, vol. 2, 1990, 41-48.
"On Taylor's conjecture for Kummer Orders" (with Ph. Cassou-Nogues ), Seminaire de la Theorie des Nombres, Bordeaux, vol. 2, 1990, 349-363.
"On Fueter model and monogenity of ring of integers" (with S. Venkataraman), J. Number Theory, vol. 43 (1), 1993, 43-50.
"Relative Galois module structure of quadratic exrensions" (with S. Venkataraman), Indian J. Pure Appl. Math., vol 25 (5), 1994, 473-488.
"Unramified quadratic extensions of real quadratic fields, normal integral bases and 2-adic L-functions" (with S. Venkataraman), J. Number Theory, vol. 67 (2), 1997, 139-145.
"Swan Modules and Hilbert-Speiser number fields" (with C. Greither , D. R. Replogle and K. Rubin ),
J. Number Theory, vol. 79 (1), 1999, 164-173.
"Normal Integral Bases, Swan Modules and p-Adic L-Functions", Number Theory for the Millennium III (Urbana, IL, 2000)
, A K Peters, Natick, MA, 2002, 231-241.
Doctoral Students ( with current affiliation)
S. Venkataraman, Ph. D., 1992; " On rings of integers of relative abelian extensions of number fields".
Dr. Venkataraman is an Assistant Professor at the IGO University in New Delhi, India.
D. R. Replogle, Ph. D., 1997; "Swan classes and realisable classes for integral group rings over groups of prime order".