Motivic Euler numbers and an arithmetic count of the lines on a cubic surface.
Hot Topics: Galois Theory of Periods and Applications March 27, 2017  March 31, 2017
Location: SLMath: Eisenbud Auditorium
Galois theory
Galois orbits
Periods
motivic integration
Euler characteristics
CayleySalmon theorem
A1homotopy theory
GrothendieckWitt group
degree formulae
PoincareHopf theorem
enumerative geometry
generalizations of classical theorems
algebraic geometry
14D24  Geometric Langlands program (algebrogeometric aspects) [See also 22E57]
53Zxx  Applications of differential geometry to sciences and engineering
0106  Proceedings, conferences, collections, etc. pertaining to history and biography
14J50  Automorphisms of surfaces and higherdimensional varieties
Wickelgren
A celebrated 19th century result of Cayley and Salmon is that a smooth cubic surface over the complex numbers contains exactly 27 lines. Over the real numbers, the number of lines depends on the surface, but Segre showed that a certain signed count is always 3. We extend this count to an arbitrary field using A1homotopy theory: we define an Euler number in the GrothendieckWitt group for a relatively oriented algebraic vector bundle as a sum of local degrees, and then generalize the count of lines to a cubic surface over an arbitrary field. This is joint work with Jesse Leo Kass
Wickelgren.Notes

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