Humans haven't been writing things down for 10,000 years, but we can get some idea of what to expect by looking at extremely ancient civilizations, namely Egypt and Mesopotamian region. Look at how badly Egyptian history from the Old Kingdom or the history of the Sumerians is remembered. In Egypt the timing of many events and the reigns and names of various pharaohs are highly uncertain, with the error bars on some events being on the scale of a few centuries. A lot of this has to do with the fact that the Egyptian calendar doesn't quite match up with the Julian one, so even when dates are recorded it's not clear when they're talking about.
Some supposed rules may be outright fictional characters misinterpreted as real. Gilgamesh was probably a real king but we know almost nothing beyond his actual reign aside from the Epic of Gilgamesh, which may have been propaganda or the result of posthumous deification. And for most of these empires the identity and reign of their rulers are some of the biggest things they are often concerned with recording for posterity. The fact that this information doesn't survive well doesn't bode well. There are entire ancient civilizations like the Elamites who despite being a large empire with their own language and writing system we basically know nothing about.
Most countries probably won't be remembered. Almost no one outside of history buffs remembers the old provinces of Rome or their pre-Roman inhabitants, even if many place names are taken from them. 10,000 years is such a long span that only the most relevant events to a future audience would be remembered. For example, the U.S. might be remembered for being the first people to land on the moon and the first to use atomic weapons in war, but the reasons for the Cold War and the nature of the war that led to the use of atomic bombs might be forgotten.
It's even plausible that highly traumatic events that we try not to forget today like the Holocaust would be forgotten. If events like the Holocaust weren't anomalous in the future it might be remembered, but given how genocide isn't an uncommon occurrence in human history there wouldn't be a lot of reason for it to stick out. The Holocaust is notable to use because it was committed by a highly industrialized, highly Westernized power in a time where genocide was no longer the order of the day, but in the far future it is unlikely that they would be Euro-centric enough to consider the actions of the Nazis and memorable relative to, say, Mao's Great Leap Forward, the Rwanda Genocide, or the actions of the Khmer Rouge.
It's unlikely a lot of art will survive, simply because art is usually a singular piece and hence can be easily misplaced or destroyed.
In general, we'd hope that people would be a bit better at having retaining information due to the widespread adoption of the printing press meaning that books no longer have to be painstakingly copied and the fact that 86% of the current population is now literate (and hence there is more demand for written materials and more reason to keep them), but the truth is a lot of what we produce now is going to be utterly unreadable in the future.
None of the languages we speak or write with now are going to be around in any recognizable form, for starters. Many ancient languages like Egyptian hieroglyphics, cuneiform, and Maya script were a pain to translate, and some like Minoan Linear A still haven't been deciphered. Paper is highly degradable, and most of the information we have on paper now is going to be rotted and gone 10,000 years from now unless some efforts have been made to recopy them into new formats.
Electronic media is also extremely fragile. Electronic media often depends on a system to run it or a long-term storage medium that can be easily damaged or corrupted. Most Internet servers will not last 10,000 years. A broken laptop sitting in the sands of the Sahara for 10,000 years may have originally had the complete works of Shakespeare, but if it can't be started it's little better than a plastic brick. Additionally the hardware to read the electronic media may not be there. Look at how much trouble people have running VCR tapes and 8-track players now, and how most computers lack CD-ROM drives or DVD players and are starting to be manufactured without USB ports. People 10,000 years from now may not have a reliable converter.
Most of what would survive would what has been carved in rock. It's been suggested that our widespread adoption of paper will be a double-edged sword for historians simply because most of what we write will degrade while many ancient cultures will have their writing stick around because they carved it into something, leaving our culture a relative enigma.
Scientific Systems May Not Last
Indeed, it's not even clear if systems we deliberately designed to last forever, such as the Linnaean system of naming or Mendeleev's periodic table will stick around, given that both are less than 300 years old. Yes, the physical principles that both describe are still around, but the names may change dramatically and their principles may be lost or re-invented from scratch or replaced with alternate models. Mendeleev I could see it being difficult to destroy, but with Linnaean species names I've already seen people try to suggest that we rename species and erase the naming contributions of many biologists because their opinions were politically incorrect by modern standards, despite the fact that the general rule is "who finds it first gets to name it" and "names are forever for stability".
Even systems of numbers might not be the same, Arabic numerals are only about 1500 years old and alternative math systems like the Maya vigesimal system or Roman numerals exist. It's conceivable that numeral systems could change in 10,000 years. Number systems might also change for political reasons (e.g., the adoption of the metric system in the wake of the French Revolution) or just because someone comes up with a better model that we don't know of yet.