Mrs Philjay and I have just come back after being away for 3 weeks or so, I came to start her car, an 06 1.4 Sport and the belt screeched as usual but this time it got worse. So much so that smoke billowed out of the bonnet. Quick check revealed the belt had melted because the alternator had seized, maybe!
Anyway, two things were revealed to me, when I started the car to more it so I could repair said belt, guess what, the battery light went OUT. Very strange, the alternator way solid so I took it off and it freed off, yeah thinks I but then horror, the thing had a huge crack in it, rats, £90.00 later all fixed, thank goodness an easy fix unlike my sons Evo which is a complete nightmare.

The original scuttle drains direct rainwater onto the alternator. There is a modified drain tube, longer, that prevents this.
https://www.fiatforum.com/grande-punto/337783-modified-scuttle-drain.html
There are other threads, do a search and you will find fuller explanations.
Need to find the longer tube to prevent it destroying the new alternator.

Yes, I know about the water and extended tube, I fitted one to my son's Evo after he knackered TWO alternators. I confess I have not changed mine. It was the fact that the warning light went out that amazes me.

Warning light for alternator is fed 12v and earths through the alternator to light the light. When the alternator turns as soon as it produces any voltage the light will dim, then extinguish completely at 12v. If due to a fault there is no earth path through the alternator, the light will not illuminate, so no light does not indicate that all is well.