Sunghan Bae
Korea Advanced Institute of Science and Technology · Mathematics
About the Lab
Professor Sunghan Bae's research focuses on arithmetic geometry and function field arithmetic, particularly in positive characteristic. His work centers on genus theory, cyclotomic function fields, and the arithmetic of $Γ$-functions in positive characteristic, drawing deep analogies to classical number theory. He investigates algebraic structures such as $Γ$-monomials, sign-cohomology, and class number problems in function fields, with significant contributions to Kummer theory and the Hasse norm principle in function field extensions. His research bridges classical arithmetic concepts with modern tools in positive characteristic, including Anderson-Thakur's methods and cohomological techniques.
Research Overview
Research Output Trend
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Selected Papers
15Abstract We study the genus theory for function fields which is the analogue of the classical genus theory developed by Hasse and Fröhlich.
Some interesting properties of Carlitz cyclotomic polynomials analogous to those of classical cyclotomic polynomials are given.
We investigate algebraic \Gamma-monomials of Thakur's positive characteristic \Gamma-function, by using Anderson-Das double complex method of computing the sign-cohomology of the universal ordinary distribution. We prove that the \Gamma-monomial associated to an element of the second sign-cohomology of the universal ordinary distribution of \mathbb{F}_{q}(T) generates a Kummer extension of the Carlitz cyclotomic function field, which is also a Galois extension of
We determine all real quadratic function fields of Richaud-Degert type with ideal class number one.
We investigate algebraic <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Gamma"> <mml:semantics> <mml:mi mathvariant="normal"> Γ </mml:mi> <mml:annotation encoding="application/x-tex">\Gamma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -monomials of Thakur’s positive characteristic <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper
Research Areas
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