Question: Alexander Vygantas was the duke of which city in Lithuania?

Context paragraphs:
Michael Glinski: Michael Glinsky (Lithuanian: "Mykolas Glinskis" , Russian: Mikhail Lvovich Glinsky , Polish: "Michał Gliński" ; 1460s – 24 September 1534) was a noble from the Grand Duchy of Lithuania of distant Tatar extraction who was also a tutor of his nephew, Ivan the Terrible.  As a young man, Glinsky served in the court of Emperor Maximilian I and earned distinction for his military service.  Around 1498 he returned to Lithuania and quickly rose in power and wealth, angering local nobles.  Just after commanding the victorious Battle of Kletsk against the Crimean Khanate in August 1506, he was accused of conspiracy against the deceased Grand Duke Alexander Jagiellon and lost all his wealth.  Glinsky began an armed rebellion against Sigismund I, the new Grand Duke.  The rebellion was unsuccessful and Glinski retreated to the Grand Duchy of Moscow, where he served Vasili III of Russia.  When the Muscovite–Lithuanian Wars renewed in 1512, Glinsky was instrumental in helping Moscow to capture Smolensk, a major trading center.  However, he was not rewarded with the regency of the city.  Angered, he planned to betray Vasili III, but the plot was discovered and he was imprisoned for 12 years.  He was freed after his niece Elena Glinskaya married Vasili III in 1526.  Before his death in 1533, Vasili appointed Elena and Glinski as protectors of his underage sons Ivan and Yuri.  Elena disapproved of Glinsky's influence in the state and had him sent to prison, where he soon died of starvation.

Lithuanian Civil War (1389–92): The Lithuanian Civil War of 1389–92 was the second civil conflict between Jogaila, King of Poland and Grand Duke of Lithuania, and his cousin Vytautas.  At issue was control of the Grand Duchy of Lithuania, then the largest state in Europe.  Jogaila had been crowned King of Poland in 1386; he installed his brother Skirgaila as ruler of Lithuania.  Skirgaila proved unpopular and Vytautas attempted to depose him.  When his first attempt to take the capital city of Vilnius failed, Vytautas forged an alliance with the Teutonic Knights, their common enemy – just as both cousins had done during the Lithuanian Civil War between 1381 and 1384.  Vytautas and the Knights unsuccessfully besieged Vilnius in 1390.  Over the next two years it became clear that neither side could achieve a quick victory, and Jogaila proposed a compromise: Vytautas would become Grand Duke and Jogaila would remain Superior Duke.  This proposal was formalized in the Ostrów Agreement of 1392, and Vytautas turned against the Knights.  He went on to reign as Grand Duke of Lithuania for 38 years, and the cousins remained at peace.

Ostrów Agreement: The Ostrów or Astrava Agreement (Lithuanian: "Astravos sutartis" , Belarusian: Востраўскае пагадненне , Polish: "Ugoda w Ostrowie" ) was a treaty between Jogaila (Władysław II Jagiełło), King of Poland and Grand Duke of Lithuania, and his cousin Vytautas the Great, signed on 4 August 1392.  The treaty ended the destructive Lithuanian Civil War, launched in 1389 by Vytautas who hoped to gain political power, and concluded the power struggle between the two cousins that erupted in 1380 after Jogaila secretly signed the Treaty of Dovydiškės with the Teutonic Knights.  The Ostrów Agreement did not stop attacks from the Teutonic Knights and the territorial dispute over Samogitia continued up to 1422.  According to the treaty, Vytautas became the ruler of Lithuania (styled Grand Duke), but he also acknowledged Jogaila's (styled Supreme Duke) rights to Lithuania.  The details of the Polish–Lithuanian relationship were clarified in several later treaties, including the Union of Vilnius and Radom in 1401 and Union of Horodło in 1413.

Mindaugas: Mindaugas (German: "Myndowen" , Latin: "Mindowe" , Old East Slavic: Мендог — "Mendog" , Belarusian: Міндоўг or Mindoūh , c. 1203 – autumn 1263) was the first known Grand Duke of Lithuania and the only King of Lithuania.  Little is known of his origins, early life, or rise to power; he is mentioned in a 1219 treaty as an elder duke, and in 1236 as the leader of all the Lithuanians.  The contemporary and modern sources discussing his ascent mention strategic marriages along with banishment or murder of his rivals.  He extended his domain into regions southeast of Lithuania proper during the 1230s and 1240s.  In 1250 or 1251, during the course of internal power struggles, he was baptised as a Roman Catholic; this action enabled him to establish an alliance with the Livonian Order, a long-standing antagonist of the Lithuanians.  During the summer of 1253 he was crowned King of Lithuania, ruling between 300,000 and 400,000 subjects.

Union of Horodło: The Union of Horodło or Pact of Horodło was a set of three acts signed in the town of Horodło on 2 October 1413.  The first act was signed by Władysław II Jagiełło, King of Poland, and Vytautas, Grand Duke of Lithuania.  The second and third acts were composed by the Polish nobility (szlachta) and Lithuanian boyars respectively.  The union amended the earlier Polish–Lithuanian unions of Krewo and Vilnius–Radom.  Politically, Lithuania received more autonomy as, after the death of Vytautas, the Lithuanian nobles could choose another Grand Duke instead of passing the title to Władysław II Jagiełło or his heir.  However, culturally, Lithuania and Poland grew closer.  Lithuania adopted Polish institutions of castellans and voivodes. Catholic Lithuanian nobles and church officials were granted equal rights with the Polish nobles and clergy.  Forty-seven selected Lithuanian nobles were adopted by Polish families and granted Polish coats of arm.  Thus the union signified the beginnings of Polonization of Lithuanian culture and the rise of the Lithuanian nobility.  It was one of the major steps towards the modernization and Europeanization of Lithuania.

Vygantas: Vygantas (baptized Alexander; Polish: "Wigunt" ; died June 28, 1392) was Duke of Kernavė.  He was one of the sons of Algirdas, Grand Duke of Lithuania (1345–1377), and his second wife Uliana Alexandrovna of Tver.

Petras Jonaitis Mantigirdaitis: Petras Jonaitis Mantigirdaitis (died after 1497) was a prominent noble of the Grand Duchy of Lithuania.  Grandson of Petras Mantigirdaitis, he first appeared in written sources in 1476 and reached his career high in 1490s when he was Voivode of Trakai (1490–97) and Grand Marshal of Lithuania (1491–97).  Chronicler Marcin Bielski described that Alexander Jagiellon was crowned and blessed as the new Grand Duke of Lithuania by the Bishop of Vilnius in 1492.  Then Mantigirdaitis presented Alexander with a naked sword and a reminder that Alexander was elected to be a just ruler.  In 1494, Mantigirdaitis was sent on the diplomatic mission to negotiate peace with the Grand Duchy of Moscow and marriage of Helena of Moscow to Alexander to end the First Muscovite–Lithuanian War.  The Bychowiec Chronicle names him as a Great Hetman who recommended Konstantin Ostrogski, the first official Great Hetman, after his death.  Therefore, it is likely that at some point Mantigirdaitis was the commander of the Lithuanian army.

Helena of Moscow: Helena Ivanovna of Moscow (Russian: Елена Ивановна ; Lithuanian: "Elena" ; Polish: "Helena Moskiewska" ; 19 May 1476 – 20 January 1513) was daughter of Ivan III the Great, Grand Prince of Moscow, and an uncrowned Grand Duchess of Lithuania and Queen of Poland as she would not convert from Eastern Orthodoxy to Catholicism.  Her childless marriage to Grand Duke of Lithuania and later King of Poland Alexander Jagiellon was a constant source of tension between the Grand Duchy of Moscow and the Grand Duchy of Lithuania.  Instead of guaranteeing peace, Helena's marriage gave her father Ivan III an excuse to interfere in Lithuanian affairs accusing Alexander of mistreating Helena and repressing Orthodox believers.  This became the pretext to renew the Muscovite–Lithuanian War in 1500.  The war ended with a six-year truce in 1503; the Grand Duchy of Lithuania lost about a third of its territory.  Despite political tensions and religious differences, the marriage was a loving one and the royal couple was close.  After her husband's death in 1506, Helena wanted to return to Moscow but was not allowed.  When she planned to run away, she was arrested and reportedly poisoned.

Kernavė: Kernavė was a medieval capital of the Grand Duchy of Lithuania and today is a tourist attraction and an archeological site (population 318, 1999).  It is located in the Širvintos district municipality located in southeast Lithuania.  A Lithuanian state cultural reserve was established in Kernavė in 1989.  In 2004 Kernavė Archaeological Site was included into UNESCO world heritage list.

Kingdom of Lithuania (1918): The Kingdom of Lithuania was a short-lived constitutional monarchy created towards the end of World War I when Lithuania was under occupation by the German Empire.  The Council of Lithuania declared Lithuania's independence on February 16, 1918, but the Council was unable to form a government, police, or other state institutions due to the continued presence of German troops.  The Germans presented various proposals to incorporate Lithuania into the German Empire, particularly Prussia.  The Lithuanians resisted this idea and hoped to preserve their independence by creating a separate constitutional monarchy.  On June 4, 1918, they voted to offer the Lithuanian throne to the German noble Wilhelm, 2nd Duke of Urach.  Duke Wilhelm accepted the offer in July 1918 and took the name Mindaugas II.  However, he never visited Lithuania.  His election stirred up controversy, divided the Council, and did not achieve the desired results.  As Germany was losing the war and was engulfed in the German Revolution, Lithuania suspended its decision to invite Duke William on November 2, 1918, thereby ending his short reign.

Supporting paragraphs: Vygantas Kernavė
Answer: Kernavė