Bounds on the Torsion Subgroups of NรฉronโSeveri
Groups
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kweon-phd-math-2021.pdf.pdf
Description
Thesis PDF
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672.81 KB
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60c504c13c21652f4abda926c205b685
Author(s)
Kweon, Hyuk Jun
Advisor(s)
Poonen, Bjorn
Date Issued
June 2021
Publisher
Massachusetts Institute of Technology
Abstract
Let ๐ โคท Pสณ be a smooth projective variety defined by homogeneous polynomials of degree โค ๐ over an algebraically closed field ๐. Let Pic ๐ be the Picard scheme of ๐, and let Picโฐ ๐ be the identity component of Pic ๐. The NรฉronโSeveri group scheme of ๐ is defined by NS ๐ = (Pic ๐)/(Picโฐ ๐)แตฃโ subscript d, and the NรฉronโSeveri group of ๐ is defined by NS ๐ = (NS ๐)(๐). We give an explicit upper bound on the order of the finite group (NS ๐)โโแตฃ and the finite group scheme (NS ๐)โโแตฃ in terms of ๐ and ๐. As a corollary, we give an upper bound on the order of the torsion subgroup of second cohomology groups of ๐ and the finite group [mathematical equation]. We also show that (NS ๐)โโแตฃ is generated by (deg ๐ โ 1)(deg ๐ โ 2) elements in various situations.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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