Combine sugar, water, vinegar, and salt in a large saucepan, and bring to a boil.
Add carrots to the brine, turn off heat, and cover the saucepan with a lid. Allow to sit 5 minutes.
Put garlic, jalapeño peppers, thyme, peppercorns, and coriander in a quart-size jar (or divide between 2 pint-size jars).
Use a slotted spoon to transfer the carrots to the jar. Pour hot brine over carrots to cover. Refrigerate for 3 days before serving. Store in the refrigerator up to 6 weeks.