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Prev. week | Sep 14–20, 2025 | Next week


Sunday,
September 14
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Monday,
September 15
15:30 Algebra and Number Theory Seminar, Kemeny 343  edit delete
Honda-Tate for K3 surfaces
Asher Auel, Dartmouth College
Deuring proved that two elliptic curves over a finite field are isogenous if and only if they have the same number of rational points, and each number of points satisfying the Hasse bound is realized.  This can be reinterpreted as saying that isogeny classes of elliptic curves are in bijection with certain Weil polynomials.  The generalization of this statement to abelian varieties over a finite field is called Honda-Tate theory.  There has been lots of interest over the last decade in establishing a Honda-Tate theory for K3 surfaces, namely, of characterizing the possible characteristic polynomials of Frobenius acting on the middle l-adic cohomology.  I'll explain recent work on this problem by myself and others, including computational work creating databases of K3 surfaces (and their zeta functions) of low degree over small finite fields, and including how noncommutative K3 surfaces play a role.
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Tuesday,
September 16
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Wednesday,
September 17
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Thursday,
September 18
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Friday,
September 19
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Saturday,
September 20
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Prev. week | September 14–20, 2025 | Next week