Question: I Cavalry Corps had a detached division that fought at the battle in which present-day country?

Context paragraphs:
VI Cavalry Corps (Grande Armée): The VI Cavalry Corps of the "Grande Armée" was the name of a French military formation that had an ephemeral existence during the Napoleonic Wars.  The corps was created on 9 February 1814 and François Étienne de Kellermann was appointed as its commander.  The corps was formed by combining a newly arrived dragoon division from the Spanish front, a second dragoon division and a light cavalry division made up of hussars and chasseurs à cheval.  The latter two divisions included units from the former III Cavalry Corps.  Kellermann led the VI Cavalry Corps in actions at Mormant, Troyes, Second Bar-sur-Aube, Laubressel and Saint-Dizier.  After Emperor Napoleon abdicated in early April 1814, the corps ceased to exist.

Battle of Waterloo: The Battle of Waterloo was fought on Sunday, 18 June 1815, near Waterloo in present-day Belgium, then part of the United Kingdom of the Netherlands.  A French army under the command of Napoleon Bonaparte was defeated by two of the armies of the Seventh Coalition: a British-led Allied army under the command of the Duke of Wellington, and a Prussian army under the command of Gebhard Leberecht von Blücher, Prince of Wahlstatt.

Fyodor Korf: Fyodor Karlovich Korf or Korff (5 April 1773 – 11 September 1823) led a Russian cavalry corps in 1812–1814 during the Napoleonic Wars.  In 1807 he led a cavalry brigade in the 4th Division at Eylau.  During the French invasion of Russia in 1812 he commanded the II Cavalry Corps at Borodino.  In 1813 he led the I Cavalry Corps at the Katzbach and Leipzig.  In 1814 he led his horsemen at Laon, Fère-Champenoise and Paris.

Reserve Cavalry Corps (Grande Armée): The Reserve Cavalry Corps or Cavalry Reserve of the "Grande Armée" was the name of a French military formation that existed during the Napoleonic Wars.  In 1805, Emperor Napoleon appointed Marshal Joachim Murat to command all the cavalry divisions that were not directly attached to the Army Corps.  During the Ulm Campaign, Murat led his horsemen in successfully hunting down many Austrian Empire units that escaped the Capitulation of Ulm.  Murat's horsemen fought at Austerlitz in December 1805.  Under Murat, the Cavalry Reserve played a prominent role in the destruction of the Kingdom of Prussia's armies after the Battle of Jena-Auerstadt in 1806.  Five dragoon divisions of the corps were employed in the Peninsular War starting in 1808 and placed under the overall command of Marshal Jean-Baptiste Bessières.  The Cavalry Reserve was reassembled in 1809 to fight Austria with Bessières still in command.  In 1812 the Reserve Cavalry Corps was split up into the I, II, III, and IV Cavalry Corps for the French invasion of Russia.

II Cavalry Corps (Grande Armée): II Cavalry Corps (Grande Armée) was a French military formation during the Napoleonic Wars.  It was first formed in December 1806, but only enjoyed a brief existence under Marshal Jean-Baptiste Bessières.  The II Cavalry Corps was reconstituted for the French invasion of Russia in 1812 and commanded by General of Division Louis-Pierre Montbrun who was killed in battle, as was his successor a few hours later.  In the War of the Sixth Coalition, General of Division Horace François Bastien Sébastiani de La Porta led the corps in 1813.  General of Division Antoine-Louis Decrest de Saint-Germain directed the corps in 1814.  During the Hundred Days, Napoleon raised the corps again and entrusted it to General of Division Rémi Joseph Isidore Exelmans.

4th Guards Cavalry Corps: The 4th Guards Kuban Order of Lenin Order of Suvorov, Order of Kutuzov Cossack Cavalry Corps was a cavalry corps of the Red Army from 1942 to 1946.  It was formed on 27 August 1942 from the 17th Cavalry Corps.  It was disbanded in 1946 by being redesignated the 4th Guards Cavalry Division.  As 4th Guards Cavalry Division, it was the last cavalry division in the Soviet Army, disbanding in 1955.

Cavalry Corps (France): The Cavalry Corps (French: "Corps de Cavalerie" ) was a French mechanized army corps established in 1939 and inactivated in 1940 after the defeat of France by Germany.  Commanded by General René Prioux, the Cavalry Corps advanced into Belgium in May 1940 and imposed significant delay on the advance of the German XVI (motorized) Corps.  Cut off by German forces from the bulk of the French Army, the corps was evacuated to England and then shipped back to France in late May and early June 1940.  Further combat resulted in significant losses of armored vehicles and a steady deterioration of the corps' combat power.  The Cavalry Corps ceased fighting as the Second Armistice at Compiègne took effect, and the corps was demobilized on July 11, 1940.

I Cavalry Corps (Grande Armée): I Cavalry Corps (Grande Armée) was a French military formation that existed during the Napoleonic Wars.  For one month in 1806–1807, Emperor Napoleon split his Reserve Cavalry Corps into the I and II Cavalry Corps.  At that time, Marshal Joachim Murat took command of the short-lived I Cavalry Corps before resuming leadership over Napoleon's Reserve Cavalry when the experiment ended.  The I Cavalry Corps was not recreated until 1812 for the French invasion of Russia when command was exercised by Étienne Marie Antoine Champion de Nansouty.  The formation fought at Borodino and Tarutino.  After being destroyed during the retreat from Russia, I Cavalry Corps was reconstituted in 1813 and Marie Victor de Fay, marquis de Latour-Maubourg was appointed to lead it.  The corps fought at Lutzen, Bautzen, Dresden, and Leipzig.  At Leipzig, Latour-Maubourg was seriously wounded and replaced by Jean-Pierre Doumerc who led the corps for the remainder of the War of the Sixth Coalition which ended with Napoleon's abdication in 1814.  After Napoleon returned from exile and retook power in France in 1815, the main French army was baptised Armée du Nord.  The army included a I Cavalry Corps led by Pierre Claude Pajol which fought at Ligny and Wavre, while one detached division fought at Waterloo.

Battle of Fairfax Court House (June 1863): The Battle of Fairfax Court House (June 1863) was fought during the Gettysburg Campaign of the American Civil War by a small Union Army cavalry detachment of two companies (87 troops) of the 11th Regiment New York Volunteer Cavalry and advance units of Confederate Major General J.E.B. Stuart's Cavalry Corps, Army of Northern Virginia.  Stuart's lead unit on the day of the battle was the 1st North Carolina Cavalry Regiment (9th State Troops) of Major General Wade Hampton's division of 2,000 men.  The main body of three divisions, often still referred to at this time as brigades, of the Confederate Cavalry Corps, about 40 percent of the total troops, was moving toward the Potomac River, soon after the start of the ride of his best divisions through and around the Union Army of the Potomac on their way to Pennsylvania.  The skirmish occurred near the village of Fairfax Court House in Fairfax County, Virginia on June 27, 1863.

Nashville Union order of battle: The following Union Army units and commanders fought in the Battle of Nashville of the American Civil War.  Order of battle compiled from the army organization during the battle (December 15–16, 1864).  The Union force was a conglomerate of units from several different departments provisionally attached to George H. Thomas’ Department of the Cumberland.  The IV Corps and the District of Etowah were permanently attached to the Department of the Cumberland while the Cavalry Corps had been attached to the Army of the Cumberland until October 1864 when it was transferred to the Military Division of the Mississippi.  The XXIII Corps was detached from the Department of the Ohio and Smith’s Corps (formerly known as the "Right Wing-XVI Corps") was detached from the Department of the Tennessee.  Other brigades and regiments from the Army of the Tennessee which were unable to rejoin their respective commands were organized into the Provisional Division and attached to the District of the Etowah.

Supporting paragraphs: I Cavalry Corps (Grande Armée) Battle of Waterloo
Answer: Belgium