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Special Cycles on GSpin Shimura Varieties

Dylan Yott

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Abstract

In this thesis we prove that a certain generating function of special cycles on GSpin Shimura varieties is modular. More specifically, we consider the Shimura variety corresponding to the reductive group $\\Res_{F/\\Q} G$, where $G=\\GSpin(V)$ the GSpin group for $V$, a quadratic space over a totally real number field $F$, $[F:\\QQ]=d$ with certain conditions at the infinite places. We construct a generating function in the sense of Kudla and Millson and show that its image in cohomology is an automorphic form.

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In this thesis we prove that a certain generating function of special cycles on GSpin Shimura varieties is modular. More specifically, we consider the Shimura variety corresponding to the reductive group $\\Res_{F/\\Q} G$, where $G=\\GSpin(V)$ the GSpin group for $V$, a quadratic space over a totally real number field $F$, $[F:\\QQ]=d$ with certain conditions at the infinite places. We construct a generating function in the sense of Kudla and Millson and show that its image in cohomology is an automorphic form.

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Available abstract

In this thesis we prove that a certain generating function of special cycles on GSpin Shimura varieties is modular. More specifically, we consider the Shimura variety corresponding to the reductive group $\\Res_{F/\\Q} G$, where $G=\\GSpin(V)$ the GSpin group for $V$, a quadratic space over a totally real number field $F$, $[F:\\QQ]=d$ with certain conditions at the infinite places. We construct a generating function in the sense of Kudla and Millson and show that its image in cohomology is an automorphic form.

Key concepts: Shimura variety, Mathematics, Pure mathematics, Automorphic form, Group (periodic table), Field (mathematics), Space (punctuation), Variety (cybernetics)

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