broadcast in Room 515, Cosmology Bldg., NTU, Online seminar
(線上演講 於台大次震宇宙館515教室直播/收播)
Exponential Sums Modulo p^m for Deligne Polynomials
Kien Huu Nguyen (K. U. Leuven)
Abstract:
Let
be a non-constant polynomial of degree
. Suppose that
is the homogeneous part of highest degree of
and the projective scheme
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associated with
is smooth. In the proof of Weil's conjecture, Deligne showed that if
is a finite field of large enough characteristic then
It is natural to ask about an analogue of Deligne's theorem for the setting of exponential sums modulo
. In this talk, I will introduce a conjecture about it together with some further application. In particular, I will present my recent result on this direction. Namely, we have
Theorem 1. Let f,d be as above. Then there is a constant c depending only on n,d such that for all large enough primes p and all m 
1 we have
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