{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86898"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86898","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Rational Points on Lattice Varieties","abstract":"Lattice varieties play an important role in several areas of mathematics. In this thesis we investigate the properties of rational points on lattice varieties over Witt vectors with algebraically closed residue field in prime characteristic. These varieties are defined over a finite field. For varieties over finite field, the local zeta function encapsulates valuable number-theoretic information about the variety. We calculate explicitly the zeta functions of these lattice varieties.","abstract_html":"Lattice varieties play an important role in several areas of mathematics. In this thesis we investigate the properties of rational points on lattice varieties over Witt vectors with algebraically closed residue field in prime characteristic. These varieties are defined over a finite field. For varieties over finite field, the local zeta function encapsulates valuable number-theoretic information about the variety. 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