None of the materials we currently have can produce a skyscraper that can last 10k years without maintenance. Not even promising materials currently on the horizon can.
Good concrete without steel reinforcement can last for a long time, but it is heavy, stiff and brittle, 10k years will likely see more than a few major earthquakes that could crumble it.
Solid rock is also quite durable, but while a good option for building something like a pyramid, it is impossible to build a skyscraper out of it.
Compressed earth is quite durable too, especially with proper care, but even without it, there are some compressed earth structures dating back thousands of years. But again, not an option for building a skyscraper.
And it goes without saying, steel won't cut it either, as "inert" as it may be it will eventually give in to weathering, corrosion, and whatnot. Some precious metals are very resistant chemically, but their mechanical properties are not suited for the task, not to mention their rarity and cost.
Plastic, albeit an environmental disaster due to the time it takes to decompose, is not an option either - it will weather, it will degrade and it will fail. Not to mention it is flammable. It will make for a hell of a torch and subsequently an infernal lake of liquid burning plastic. Plastic might be used to encase steel frames, which will protect the steel from the elements for a while, but only until the plastic weathers to the point of cracking. Also plastic is usually soft, so any abrasive particles in the air would affect it.
You basically don't want to use for a skyscraper anything other than steel frame structure. Not for skyscrapers are we understand the term today, much less compared to some futuristic standards. Definitely not concrete. The big challenge here is protecting steel from corrosion. Corrosion resistant alloys get you only halfway. Paint will weather and crack, a plastic coating will weather and crack. Steel must be protected by something that is:
- moisture resistant and water repellent
- resistant to weathering and corrosion
- hard enough to withstand wind abrasion
- flexible enough to not crack and crumble as the structure flexes due to winds, quakes, and thermal expansion/contraction and as in time sags, which it will
Extreme density rock wool comes to mind here. It can be infused with steel frames in the early production stage at a molecular level, when the steel is still red hot, using an extrusion process. It can be treated with mineral oils to protect from moisture, and its external layer can be partially molten to form a hard protective crust. Granted, oil will eventually weather off, but that can be fixed by providing extra oil in reservoirs so that oil content can be replenished through gravity and capillary action. Even at high density, the wool will not be a rigid solid internally, and while the outside will inevitably crack in time, it will not crumble as the fiber will be holding it together. The purpose of the external shell is only to protect from abrasive winds and wool disintegration, the mineral oil on the inside is what protects from corrosion. Mineral wool is also a great insulator, which will reduce the severity of thermal stresses, it is cheap, abundant and recyclable. The steel structure itself must not use any bolts or welds but instead be held together entirely by a modular construction and its weight.
Earthquakes are the big obstacle to using materials, which would otherwise be good candidates due to their resistance to weathering. But if you are willing to go offshore, and of solid ground, you could have floating megastructures that would be immune to quakes. Granted, they won't be skyscrapers in the context of towers, more like floating bubbles, but they could get to formidable proportions. It is doable through additive manufacturing. The material could be tempered glass. Such a bubble will have the advantage of encapsulating a huge amount of space, providing natural sunlight, and creating the conditions to have an entire ecosystem isolated from the outside world, meaning that it could potentially survive a broad range of disasters, basically everything aside from a dense and continuous comet shower. Artificial lighting could even help sustain the ecosystem in the event of a temporary solar blackout, in the case of global volcanic eruption or nuclear winter. At that scale of construction, tsunamis will have the destructiveness taken out of them, using nuclear reactors the structure will be able to sustain life for hundreds or even thousands of years in a world that is otherwise inhospitable to life. Measures must be taken not to hit rock or get beached, that can be achieved either by anchoring somewhere in oceans' dead spots (plenty of floating plastic there that can be recycled as well) or by making the structure capable of sailing, and in case of loss of occupants, equip it with an auto-pilot software that will keep it off the shores by using nuclear reactors or renewable power sources.
Now if we get maintenance back into the equation, it should at least theoretically be possible to make a skyscraper that can last 10k years. It doesn't have to be human maintenance though, it could be a team of robots, which use renewable power and have enough materials to self-produce for 10k years. That's at least somewhat plausible.
The other viable option, a little more in the sci-fi realm, but still somewhat conceivable would be an engineered artificial life organism, something like a mega tree, but more resilient to the elements and elementals. It will essentially be self-maintaining, replacing weathered and compromised material at the nano-scale level, pretty much the organic version of the "robot maintenance" version above. However, that would be quite challenging, creating artificial and fully functional life aside, it will also have to be:
- immune to time, effectively immortal
- immune to fire
- immune to extremely hot and extremely cold
- immune to arid or wet climate
- immune to diseases as in system malfunctions
- immune to pH imbalances
- immune to full solar blackouts
- immune to viral and bacterial infections
- immune to a wide range of pests, from bacteria through termites, cockroaches, rats and everything that may eat it
Those challenges aside, if we presume that this is doable, such an organism can be employed into a variety of beneficial ways, for example, grow food, purify toxic water and air for the inhabitants, even grow electronic circuits, computers and communication systems and whatnot.