Exposé on a conjecture of Tougeron

Becker, Joseph. "Exposé on a conjecture of Tougeron." Annales de l'institut Fourier 27.4 (1977): 9-27. <http://eudml.org/doc/74342>.

@article{Becker1977,
abstract = {An algebra homomorphism of the locatized affine rings of an algebraic variety is continuous in the Krull topology of the respective local rings. It is not necessarily open or closed in the Krull topology. However, we show that the induced map on the associated analytic local rings is also open and closed in the Krull topology. To do this we prove a conjecture of Tougeron which states that if $\eta $ is an analytic curve on an analytic variety $V$ and $f$ is a formal power series which is convergent when restricted to all curves $\eta ^\{\prime \}$ on $V$ near $\eta $ (in the Krull topology), then $f$ is convergent when restricted to $V$.},
author = {Becker, Joseph},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {4},
pages = {9-27},
publisher = {Association des Annales de l'Institut Fourier},
title = {Exposé on a conjecture of Tougeron},
url = {http://eudml.org/doc/74342},
volume = {27},
year = {1977},
}

TY - JOUR
AU - Becker, Joseph
TI - Exposé on a conjecture of Tougeron
JO - Annales de l'institut Fourier
PY - 1977
PB - Association des Annales de l'Institut Fourier
VL - 27
IS - 4
SP - 9
EP - 27
AB - An algebra homomorphism of the locatized affine rings of an algebraic variety is continuous in the Krull topology of the respective local rings. It is not necessarily open or closed in the Krull topology. However, we show that the induced map on the associated analytic local rings is also open and closed in the Krull topology. To do this we prove a conjecture of Tougeron which states that if $\eta $ is an analytic curve on an analytic variety $V$ and $f$ is a formal power series which is convergent when restricted to all curves $\eta ^{\prime }$ on $V$ near $\eta $ (in the Krull topology), then $f$ is convergent when restricted to $V$.
LA - eng
UR - http://eudml.org/doc/74342
ER -