Hasse–Witt matrices for polynomials, and applications
Rendiconti del Seminario Matematico della Università di Padova, Tome 145 (2021), pp. 117-152.
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In a classical paper, Manin gives a congruence [15, Theorem 1] for the characteristic polynomial of the action of Frobenius on the Jacobian of a curve , defined over the finite field , , in terms of its Hasse–Witt matrix. The aim of this article is to prove a congruence similar to Manin’s one, valid for any -function associated to the exponential sums over affine space attached to an additive character of , and a polynomial . In order to do this, we define a Hasse–Witt matrix , which depends on the characteristic , the set of exponents of , and its coefficients. We also give some applications to the study of the Newton polygons of Artin–Schreier (hyperelliptic when ) curves, and zeta functions of varieties.
@article{RSMUP_2021__145__117_0,
author = {Blache, R\'egis},
title = {Hasse{\textendash}Witt matrices for polynomials, and applications},
journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
pages = {117--152},
volume = {145},
year = {2021},
doi = {10.4171/rsmup/74},
mrnumber = {4261649},
zbl = {1479.11157},
language = {en},
url = {http://www.numdam.org/articles/10.4171/rsmup/74/}
}
TY - JOUR AU - Blache, Régis TI - Hasse–Witt matrices for polynomials, and applications JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2021 SP - 117 EP - 152 VL - 145 UR - http://www.numdam.org/articles/10.4171/rsmup/74/ DO - 10.4171/rsmup/74 LA - en ID - RSMUP_2021__145__117_0 ER -
Blache, Régis. Hasse–Witt matrices for polynomials, and applications. Rendiconti del Seminario Matematico della Università di Padova, Tome 145 (2021), pp. 117-152. doi : 10.4171/rsmup/74. http://www.numdam.org/articles/10.4171/rsmup/74/
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