Helm

Shortly after the conclusion of a war that destroyed the Earth, rendering it uninhabitable for generations, the survivors in the grossly-overstretched lunar colony decide to send four thousand in a colony ship to a planet that had been in the process of being terraformed. However, the colony ship was only designed to carry one thousand -- and the other three thousand replace the supplies that the colony would have needed to start on the new planet as a technological civilization. The colony will survive ... but they will survive as a low-tech civilization that will have to rebuild to a higher level. And to help them, they will begin the job implanted with a strict religious code, designed to maximize the probability of the colony's survival.

Generations later, the story resumes on the now-terraformed planet with Leland de Laal, the youngest son (at just under seventeen) of the high steward of the prosperous house of Laal, defying the proclamation of his father to climb a granite pillar to reach the legendary Helm that sits atop it -- a choice which will thrust him into the midst of machinations far beyond his prior imaginings.

Written by Steven Gould, the author better known for writing the book Jumper. Falls in the Speculative Science class on the Mohs Scale of Science Fiction Hardness.

Tropes used in Helm include:

Apocalypse How: On a planetary scale on Earth, somewhere just shy of total extinction, due to antimatter bombs dropped during a war.
Badass Bookworm: Leland, who had spent almost all his spare time prior to donning the Helm in the library, reading.
Book Ends: The first chapter of the book is the survivors of Earth sending a colony ship to Agatsu. The last chapter is a report, sent back to Earth, that the colony is successful.
Born in the Saddle: The Rootless clans.
Brainwashed:
- First, on Earth, the impetus for the earth-destroying war was the use of imprinters to force religious conversions.
- Second, under the category of Brainwashing for the Greater Good, the use of imprinters on the colonists.
- Third, the use of the Helm, which was the last of the surviving imprinters, by Sigfried of Cotswold after capturing Laal Station to convert key persons into traitors for his side.
Casual Danger Dialog: Leland engages in this with Marilyn while retaking Laal Station.
Chekhov's Gun: The nook in Laal's library that Leland shows Marilyn.
Deadly Dodging: Leland learns this during his Training from Hell.
Double Meaning: When Denesse Sensei meets Leland, everything he says about the steeping of the tea is simultaneously a comment on Leland's absorption of the effects of the Helm.
Earth-That-Was: After the war.

The temperature at Earth's equator hovered around 4 degrees Centigrade. Snowstorms and high-altitude dust clouded the planet.

Exactly What It Says on the Tin: Leland's mounted infantry unit, The Eight Hundred.
Fantasy Gun Control: All explosives have been outlawed on Agatsu by general agreement.
Heroic Sacrifice: Ricard de Laal.
Horse Archer: Many, but it is widely agreed that the Rootless are the best.
Human Popsicle: The settlers, being transported to Epsilon Erdani II from the Moon.
Old Master: Dr. Michaela Herrin, akido expert.
Out-Gambitted: Arthur de Noram, trying to scheme with Siegfried Montrose -- and both of them versus the de Laals, pater et filius.
Reluctant Warrior: Leland becomes this when he is made captain of a unit of eight hundred soldiers. He spends a fair amount of time mourning the deaths even of enemy soldiers invading his homeland.
The So-Called Coward: Leland.

Dulan: [wrapping up a description of Leland's foibles] He does pursue whatever interests him with a passion. But he never stands up for himself.
Malcolm: Oh? Is he beaten regularly?
Dulan: No, he backs away whenever there is any sort of confrontation.
Malcolm [smiling]: Maybe he knows more about fighting than you think.

Space Station: The moon base, designed for six hundred, holding -- prior to the colony's departure -- seven thousand.
Take Over the World: Siegfried's ambition.
Terraform: Epsilon Erdani II -- Agatsu -- is terraformed prior to the colony's landing.
Training from Hell: Dulan de Laal subjects his son Leland to this after Leland wears the Helm.
Treachery Cover-Up: Arthur de Noram is permitted to retire rather than be revealed as the one who allowed Cotswold to invade Laal.
Upgrade Artifact: The Helm. Unusually, it does not induce Instant Expertise.
Writers Cannot Do Math: Two errors in the calculation of ages, and a third possible in the calculation of mass:
- Marilyn de Noram is first described, through Leland's eyes, as a young woman who "couldn't have been much older than Leland" (two years older, it is later revealed). Later, Dulan de Laal says that Dillan de Laal is "fifteen years older" than Marilyn. In the family tree at the beginning of the book, Leland is 17 and Dillan is 27.
- At another point, it is said that when Dulan was 25, Dillan was 2 and Dexter "a slight swelling in his mother's figure". Dillan is in fact listed as three years older than Dexter (27 and 24), but Dulan is listed as 52.
- The Floating Stone at Laal Station is described as "a single piece of granite carved in the shape of a half cylinder" four meters high and five meters in diameter, and is stated to weigh thirty-seven metric tons. A solid granite half-cylinder of those dimensions would have a volume of thirty-nine cubic meters and weigh over one hundred metric tons. That said, the text does not strictly specify that the cylinder is solid -- and a half-cylindrical granite shell fifty centimeters thick would have the specified mass.