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K-theory of certain additive categories associated with varieties

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thesis
posted on 23.07.2021, 19:46 by Harrison WongHarrison Wong
Let K0(Vark) be the Grothendieck group of varieties over a field k. We construct an exact category, denoted Add(Vark)S, such that there is a surjection K0(Vark)→K0(Add(Vark)S).If we consider only zero dimensional varieties, then this surjection is an isomorphism. Like K0(Vark), the group K0(Add(Vark)S) is also generated by isomorphism classes of varieties,and we construct motivic measures on K0(Add(Vark)S) including the Euler characteristic if k=C, and point counting measures and the zeta function if k is finite.

History

Degree Type

Doctor of Philosophy

Department

Mathematics

Campus location

West Lafayette

Advisor/Supervisor/Committee Chair

Deepam Patel

Additional Committee Member 2

Donu Arapura

Additional Committee Member 3

Kenji Matsuki

Additional Committee Member 4

Saugata Basu

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