MIT Number Theory Seminar

Tuesday, September 28, 2021 at 4:30am to 5:30am

MIT, 2-143

Speaker:  Bianca Viray (University of Washington)

Title:  Quadratic points on intersections of quadrics

Abstract:  A protective degree 𝒹 variety always has a point defined over a degree 𝒹 field extension.  For many degree 𝒹 varieties, this is the best possible statement, that is, there exist classes of degree 𝒹 varieties that never have points over extensions of degree less than 𝒹 (nor even over extensions whose degree is nonzero modulo 𝒹).  However, there are some classes of degree 𝒹 varieties that obtain points over extensions of smaller degree, for example, degree 9 surfaces in ℙ 9 , and 6-dimensional intersections of quadrics over local fields.  In this talk, we explore this question for intersections of quadrics.  In particular, we prove that a smooth complete intersection of two quadrics of dimension at least 2 over a number field has index dividing 2, i.e., that it possesses a rational 0-cycle of degree 2.  This is joint work with Brendan Creutz.


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Bjorn Poonen, Number Theory Seminar, Number_Theory_Seminar, Wei Zhang, Andrew Sutherland


Department of Mathematics


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