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Семинар отдела алгебры и отдела алгебраической геометрии (семинар И. Р. Шафаревича)
2 марта 2021 г. 15:00, г. Москва, online
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Some quadratic conductor formulas
(joint work with Pepin Lehalleur and Srinivas)
M. Levine |
Количество просмотров: |
Эта страница: | 237 | Видеофайлы: | 5 | Материалы: | 43 |
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Аннотация:
A smooth projective variety over a
field k defines a dualizable object in the motivic stable homotopy
over k, and thereby an Euler characteristic in the endomorphism ring
of the unit. A theorem of Morel identifies this endomorphism ring
with the Grothendieck-Witt ring of quadratic forms over k and with
A. Raksit, we have shown that this quadratic Euler characteristic is
given by the intersection form on Hodge cohomology. We use the
computation of Hodge cohomology of hypersurfaces via the Jacobian
ring to give an explicit description of the categorical Euler
characteristic of a smooth hypersurface and use this to give
examples of a quadratic conductor formula for certain
degenerations. There are mysterious "error terms" that makes the
formula deviate from what one might expect at first glance. These
error terms disappear over the complex numbers and also over the
real numbers, but are in general non-zero.
Дополнительные материалы:
quadratic_conductor_formulas.pdf (8.8 Mb)
Язык доклада: английский
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